WASHINGTON — Governors across the United States struggled Monday with how to make good on President Donald Trump’s order that their economically battered states deliver billions more in unemployment benefits to jobless residents.

Democrats were harshly critical of Trump’s order, which he signed Saturday night after talks with Congress on a broad new pandemic aid package collapsed. But even Republican governors said the order could put a serious strain on their budgets and worried it would take weeks for tens of millions of unemployed Americans to begin seeing the benefit.

Congress initially provided a $600-a-week supplement to unemployment benefits when the coronavirus pandemic shut down much of the United States in March. But that benefit lapsed July 31, after talks between the White House and Congress broke down. Republicans had pushed for a $400 supplemental benefit, Democrats said it was not enough, and so Saturday Trump ordered the $400 benefit — but said it was contingent on states coming up with $100 of that.

Gov. Andrew Cuomo of New York told reporters Monday that Trump’s directive would cost his state about $4 billion by the end of the year, making it little more than a fantasy. He said that no New Yorker would see enhanced unemployment benefits because of the president.

“This only makes a bad situation worse,” Cuomo said. “When you are in a hole, stop digging. This executive order only digs the hole deeper.”

His comments were echoed by Gov. Andy Beshear of Kentucky, a Democrat like Cuomo, who said Trump’s order would cost his state $1.5 billion through the end of the year.

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“It’s not workable in its current form,” Beshear said. “It’s something virtually no state can afford.”

Republicans largely praised the president for trying to act where Congress’ dysfunction had failed, but they said they would need to pull funds from other pressing budgetary needs.

Gov. Asa Hutchinson of Arkansas, a Republican, said it was possible to comply with Trump’s executive order, but he would have to reallocate money from another portion of the budget.

“We could do it,” Hutchinson said in an interview. “It would be a readjustment of priorities and take some time.” He added, “That’s not ideal.”

Gov. Brian Kemp of Georgia, a Republican and an ally of Trump, said his staff was still working through what to do about unemployment benefits. “We’re digging in on that issue,” he said.

And Gov. Jim Justice of West Virginia, a Republican, said the order would cost his state $26 million a week.

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“The question of whether or not West Virginia will be able to pay that, whether or not West Virginia will willingly pay that, I would tell you hands down, period — period — we’re going to pay that,” Justice said during a news conference. “We cannot let our people that are sitting out there with no job wondering what in the world they are going to do, sit out there and wilt on the vine.”

Still, Justice said he remained hopeful that the federal government would decide to cover the whole cost of the program and that lawmakers would strike a deal. “We hope Congress will quit being a bunch of political babies,” he said.

In the meantime, Trump appeared to be making cascading changes to the policy on the fly, with the result that some unemployed people could receive only a $300 supplemental benefit per week. Officials in the office of Gov. Mike DeWine of Ohio, a Republican, said they were told late Sunday by the Labor Department that there was a new option that allowed unemployed workers to claim the additional $300 per week without the state kicking in an extra $100.

DeWine opted to just take the federal money. “It’s a lot quicker to implement and get the benefits to Ohioans at no additional cost to the state,” said Dan Tierney, a spokesman for DeWine.

Several other states confirmed Monday that they had received the same option from the Labor Department, although how many would actually get it remained an open question Monday evening, when Trump told reporters that he would waive the 25% match in certain cases.

“We just had a meeting with the governors, and they were very anxious to get money for the people in their states,” Trump said at a White House briefing. “We can terminate the 25%, or we don’t have to do that. So we will see what it is — depends on the individual state — but a lot of money will be going to a lot of people very quickly.”

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Treasury Secretary Steven Mnuchin, who was with the president at the briefing, said the benefit would begin to go out to unemployed workers within the next week or two. But it was also unclear how long that federal benefit would last, with some experts estimating it would be just a few weeks because the administration could direct only existing funding.

As the governors wrestled with Trump’s order, talks on a congressional aid package remained at a standstill. Several House and Senate members have scattered across the country unless they are called back to vote on an agreement. They spent the day trading barbs over who was to blame for the logjam.

In an interview with CNBC on Monday, Mnuchin, who has been negotiating for the Trump administration, declined to comment on specifics but said that the White House remained ready to make a deal.

He urged Democrats to consider a limited package focused on areas of agreement such as funding for schools — an entreaty Democrats have repeatedly rejected, arguing that the toll of the pandemic warrants a sweeping, broad package and urging Republicans to consider more than doubling their $1 trillion proposal.

“There’s a deal to do if the Democrats are reasonable and want to compromise,” Mnuchin said. “If their attitude is we’d rather give you nothing than agree on things, then we’re not going to get a deal.”

Sen. Chuck Schumer of New York, the Democratic leader, told reporters Monday that progress was incumbent on administration officials deciding “to change and meet us in the middle” and “not say it’s their way or no way.”

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“The Democratic position is that we want to devote enough resources to defeat the virus and see the American people through this crisis,” Schumer said in a speech on the Senate floor.

Republicans, who face stark divisions within their own conference over the scope of another relief package, accused Democrats of prioritizing long-standing political goals over reaching a compromise for aid.

“They think they have political leverage over the president of the United States, and so they’re willing to personally increase the pain for vulnerable families unless they get their way on matters not related to COVID-19,” Sen. Mitch McConnell of Kentucky, the majority leader, said on the Senate floor Monday afternoon. “Democrats said, ‘Our way or the highway.’ ”

Unemployment remains stubbornly high, even after states lifted restrictions and allowed stores, restaurants and other industries to reopen. The government reported last week that nearly 1.2 million workers had filed new claims for state unemployment benefits, the lowest weekly total since March, but still high by historical standards. Economists estimate that about 30 million people are still collecting unemployment.

Even before Trump’s actions Saturday, several state and local governments, reeling from lost tax revenue as a result of the pandemic-induced economic collapse, were already lobbying Congress to allocate billions more in relief. A $2.2 trillion stimulus law approved in March set aside a $150 billion pot of money for state and local governments, but the funds came with cumbersome restrictions and prevented municipalities with less than 500,000 people from directly receiving relief.

State tax revenue was down more than 20% in May from a year earlier, according to data from 46 states compiled by Lucy Dadayan, a researcher at the Urban Institute. She estimated revenues could fall by $200 billion in the 2020 and 2021 fiscal years. State and local governments have already cut more than 1 million jobs during the crisis, and many economists fear more layoffs if the federal government does not provide billions in aid.

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In the $3.4 trillion legislation that House Democrats approved in May, lawmakers allocated close to $1 trillion for state, local and tribal governments, and top Democrats have continued to hold firm in their insistence that those governments need substantial relief. Some lawmakers have coalesced around a bipartisan proposal that would provide $500 billion in new relief, in addition to loosening flexibility on how the previously allocated money is spent.

But Republicans, arguing that much of that money had not yet been spent, did not include any new aid for states in their own $1 trillion proposal, with some local governments reporting a delay in getting relief from their state governments. The Treasury Department’s inspector general office reported in late July that states had spent only about one-quarter of the aid provided, but some state officials and experts said the report did not account for money that was already earmarked for spending.

Trump, who has largely sidelined himself during talks on Capitol Hill, asserted that Democrats were ready to make a deal and touted a rise in the stock market Monday. He also called for cutting capital gains taxes and more unspecified tax cuts for the middle class.