With days to go before enhanced jobless benefits expire, the White House and Senate Republicans are struggling to design a way to scale back the program without overwhelming state unemployment agencies and imperiling aid to more than 20 million Americans.

The hang-up has led to an abrupt delay in the introduction of the GOP’s $1 trillion stimulus package. The White House and Democrats have said they want a deal by the end of the month, but Senate Majority Leader Mitch McConnell (R-Ky.) suggested Friday that reaching an agreement could take several weeks, a timeline that could leave many unemployed Americans severely exposed.

“Hopefully we can come together behind some package we can agree on in the next few weeks,” McConnell said at an event in Ashland, Ky.

Part of the problem stems from a push by administration officials and GOP lawmakers to reduce a $600 weekly payment of enhanced federal unemployment benefits. The White House and the GOP disagree about how to do this, and talks remain highly contentious. They hope to release a proposal early next week.

“We realize there are a lot of hard-working Americans because of covid [who] still won’t have jobs,” Treasury Secretary Steven Mnuchin told reporters Thursday.

After convulsing in March and April when the coronavirus pandemic shut down large parts of the United States, the economy showed signs of regaining its footing before sliding again in recent weeks. The effects of numerous stimulus programs appear to be wearing off, and the pace of layoffs has picked up again. Layoffs that many Americans thought would be temporary have dragged on and become permanent, particularly as new cases of the novel coronavirus surge in parts of the country.

This has put enormous pressure on state unemployment programs, which typically pay out about 45 percent of a worker’s prior wages. In March, Congress approved the $600-per-week emergency bonus for every unemployed worker on top of that traditional payment, funneling hundreds of billions of dollars to newly jobless Americans as the pandemic hit the country.

That federal benefit, being received by more than 20 million people, is to expire at the end of this month. And the expiry comes as a federal eviction moratorium also is ending, creating a dynamic that could greatly stress cash-strapped families.

In practice, the coming lapse in the jobless benefit means millions of workers are receiving their last enhanced benefit payment this week.

In recent days, senior congressional Republicans and Mnuchin have discussed replacing this universal federal bonus with one tied to workers’ incomes before their jobs were lost. Instead of sending a $600-per-week bonus to every unemployed person, under this plan, the federal government would provide a bonus amounting to about half of the existing state support, according to three senior GOP officials, who spoke on the condition of anonymity to describe fast-moving and internal deliberations.

Mnuchin and President Trump have said publicly that they want to have the new payments replace roughly “70 percent” of a worker’s prior income. This would represent a combination of the nearly 50 percent state contribution of a worker’s prior income plus 25 percent kicked in by the federal government. Republican lawmakers have discussed extending the flat payment at about $200-per-week instead of $600 to give the states time to adjust to the new formula and system.

“We are going to extend it on the basis of wage replacement; it’s approximately at 70 percent of wage replacement,” Mnuchin told reporters Thursday about the Republican proposal.

Other leading Republican lawmakers have argued for cutting the $600-per-week bonus down to $200-per-week, these people said, with one possibility being that this amount slowly phases out over time. These GOP officials have insisted that targeted wage replacement could prove too difficult for the states to implement.

One Senate Republican aide close to the negotiations, who spoke on the condition of anonymity to discuss internal matters, said that a $200 flat payment represented the party’s “default” position, with additional funding included to help states upgrade their unemployment systems. The aide played down the odds of the GOP’s approving the more complicated replacement instead of the $200-per-week extension.

The issue has contributed to a delay in the introduction of the $1 trillion stimulus package McConnell had planned to release this week. Republicans debated last-minute changes to the unemployment insurance section of the proposal, according to the three people aware of the deliberations.

The proposed legislation could come on Monday, a lag that has prompted scorching criticism from congressional Democrats who have been demanding action for months. Congress has not passed any coronavirus relief legislation since approving four bipartisan bills in March and April that pumped around $3 trillion into the economy. McConnell wanted to wait to see how the unemployment benefits and other programs approved in that unprecedented stimulus effort played out before taking additional action.

“This weekend, millions of Americans will lose their unemployment insurance, will be at risk of being evicted from their homes, and could be laid off by state and local government, and there is only one reason: Republicans have been dithering for months while America’s crisis deepens,” House Speaker Nancy Pelosi (D-Calif.) and Senate Minority Leader Charles E. Schumer (D-N.Y.) said in a joint statement Friday.

If adopted, the new unemployment plan could complicate negotiations with congressional Democrats, who favor extending the $600 weekly payment through January. And it’s unclear if balky state processing systems would have the capacity to implement a complicated new formula on such short notice.

“We’re dealing with the mechanical issues associated with that,” Mnuchin told reporters about the wage replacement plan.

The proposal would, in key respects, meet the conflicting political and economic pressures bearing down on the GOP and White House as the unemployment deadline looms for millions of Americans months away from Election Day.

Senate Republicans and White House officials have been clear that they are not willing to extend the $600-per-week benefit, which conservatives and many business organizations say encourages people to stay home rather than work. Many economists dispute this notion. Senior Republicans have also said they do not want additional federal unemployment benefits to go away entirely, acknowledging that some additional federal help should still be provided to those made jobless during the pandemic. The benefits are politically popular, with a recent Washington Post-ABC News poll finding close to 60 percent of Americans supporting their extension.

“We need to make sure unemployment insurance is continued,” McConnell said Friday. “There is a controversy, however, over whether the provision in the previous measure that allowed people to make more money staying at home than going back to work was a good idea. That’s not going to be our recommendation. But I do think basic unemployment insurance — fundamentally handled by the states but backed up by us — will be a part of” the GOP package.

Trump and Mnuchin have characterized their proposed solution, replacing “70 percent” of a worker’s prior income, as a reasonable middle ground. At his White House news briefing Tuesday, Trump expressed ambivalence about the benefit but said it would be partially extended.

“The employers are having a hard time getting [employees] back to work. ... I was against that original decision, but they did that. It still worked out well because it gave people a lifeline, a real lifeline. Now we’re doing it again,” the president said. “They’re thinking about doing 70 percent of the amount. The amount would be the same, but doing it in a little bit smaller initial amounts.”

Congressional Democrats and many economists say the current benefit should be extended in full to prevent a crucial stimulus from disappearing from an already wobbly economic recovery.

Given the difficulty of reaching a deal with Democrats before the existing benefits expire, Mnuchin and White House Chief of Staff Mark Meadows on Thursday floated a stand-alone extension of unemployment provisions as part of a package with school funding and a type of lawsuit shield to make it harder for employees to sue their employers if they become sick with the novel coronavirus.

Senior lawmakers in both parties oppose this piecemeal approach, but if they are unable to reach a deal, they might be forced to pass some type of stand-alone benefit extension next week.

In March, lawmakers initially discussed increasing unemployment benefits so they would represent 100 percent of a worker’s prior income. Congress ultimately abandoned the idea in favor of the universal $600 bonus, in part because Labor Secretary Eugene Scalia warned that the nation’s unemployment systems could not handle the complexity of matching every individual’s unemployment benefits to the person’s prior income, according to Sen. Ron Wyden (D-Ore.), who led those negotiations.

“Scalia said, ‘It can’t be done,’ ” Wyden said in an interview. “We have not seen a single piece of paper describing how this would be administered without the downsides Scalia pointed out months ago.”

Mnuchin acknowledged the technical challenges posed by converting from one system to another when addressing reporters on Thursday. He said the matter was being discussed with state unemployment offices. “Let me just say, different states are in different places,” Mnuchin said. “Some states can implement this quickly. Some states will take time."

Some experts are skeptical. State unemployment offices have been badly overwhelmed by the unprecedented surge in claims, and there were another 1.4 million claims last week. Thousands of the newly jobless have struggled for months to obtain benefits and in some states have camped outside unemployment offices overnight to be ahead in line for help.

The $600-per-week bonus was chosen for its simplicity compared with targeted, individual wage replacement — but it has proved tremendously difficult for states to implement as the nation’s unemployment rate spiked to 15 percent before falling to 11 percent.

“You’re asking states to overhaul their insurance systems in the middle of a pandemic, when they’re already overloaded. What happens if states shift to a new system and they dump beneficiaries and miss payments because of an error?” said Ernie Tedeschi, who served as an economist in the Treasury Department under the Obama administration. “It’s too complicated.”

Andrew Stettner, a senior fellow at the Century Foundation, said that states would do their best to deliver but that many would struggle to pull off the change. “The state [unemployment insurance] systems are like a house built on sticks and you’re throwing a match onto them,” he said. Stettner added that it could prove difficult for the Labor Department to figure out how to target payments for every state to reflect 70 percent of the wage of every person.

White House and GOP officials have discussed a transition period that would give states time to figure out how to implement the reduction in benefits. Under this scenario, Republicans could first extend the benefit at a lower amount of about $200 per week instead of $600, continuing the existing flat payment at a reduced level. Democrats would be sure to demand a higher figure.

The $200 bonus, combined with state benefits, would amount to close to 70 percent of a typical worker’s prior income, although under the flat-amount formula, there would be significant variation, as some would receive more than prior income and some would receive less.

“There’s a way to extend this so the majority of people will get paid the 70 percent immediately,” Mnuchin said. Meadows added that the $1,200 stimulus payments expected to be included in the package would help make up the difference for Americans for whom the extension does not amount to 70 percent of prior income.

At the end of a period that may last two months, one senior GOP congressional official said, the automatic payment would go away and be replaced by the more-targeted benefit.

“After two months, the states say — at least most states; I think pretty much all states — say they could convert to the feds doing a percentage of the state benefit,” said the GOP official, who spoke on the condition of anonymity to discuss internal deliberations. “Do your state calculation, and then the [federal government] will do 50 percent on top of that.”

Whether the states will be able to pull off the change in a way that protects beneficiaries remains to be seen. The National Association of State Workforce Agencies recently said that most states would need one to four weeks even to change the bonus amount from $600 to some other amount, according to Wyden’s office.