Democratic leaders late Thursday said they rejected a short-term proposal offered by top White House negotiators to replace lapsed unemployment benefits while broader coronavirus relief measures are left for later.

“We just don’t think they understand the gravity of the problem,” Senate Minority Leader Charles E. Schumer said after a two-hour meeting with Speaker Nancy Pelosi, Treasury Secretary Steven Mnuchin and White House Chief of Staff Mark Meadows.

“I think they understand that we have to have a bill, but they just don’t realize how big it has to be,” Pelosi said.

President Donald Trump earlier this week floated the possibility of renewing supplemental unemployment benefits temporarily, as well as extending an expiring moratorium on evictions from federally backed housing. Democratic leaders rejected a similar offer at a meeting Wednesday, and it wasn’t immediately clear what new ideas Mnuchin and Meadows brought to the table Thursday.

Their proposals “were not received warmly,” Meadows said.

It was the fourth meeting in as many days between the four principals, which haven’t included the top Republicans on Capitol Hill, who for now are leaving the negotiations to Trump’s deputies. More talks are set for Friday and possibly Saturday as well, Mnuchin said.

“We are working around the clock to see if we can reach an agreement that’s good for the American people,” Mnuchin said.

Congress passed and Trump signed into law the $600 supplemental weekly benefit in March; the provision expires Friday, but in reality millions already received their last checks.

Meadows sounded grim about the state of play. “I think the Democrats are willing to allow the enhanced unemployment to expire,” he said. “I’m not very optimistic on anybody who’s counting on enhanced unemployment to have any relief anytime soon.”

Gears turning

Senate Republicans did get the procedural gears turning Thursday to set up potential votes on partially reviving expanded unemployment benefits, and potentially other COVID-19 relief measures.

Majority Leader Mitch McConnell made a procedural move Thursday to get a House-passed bill, intended to be the legislative vehicle, pending before the Senate.

“It makes it the pending business for next week. And we can keep talking and hopefully making progress because no progress is being made anywhere else,” McConnell said outside the Senate chamber.

“My understanding is that it’s a message from the House and takes 51 votes to get on it. And then we can take up the extension of unemployment benefits. And we’ll see whether our Democratic friends are serious about doing that or not. And then the Senate could work its will, whatever could get 60,” said Sen. John Cornyn, R-Texas.

Under that process, McConnell avoided needing any Democratic votes to overcome a filibuster on proceeding to the legislation, but any amendments would face 60-vote hurdles. The method can be used to get senators on record supporting or opposing specific proposals.

The “shell” bill McConnell called up was an unrelated measure that passed both chambers already dealing with Uighur human rights in China, which became law as part of separate legislation last month. The motion to proceed was agreed to, 47-42.

Several GOP senators told reporters they expected the first amendment in line for a test vote as early as Monday would be from Republicans Ron Johnson of Wisconsin and Mike Braun of Indiana.

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That would provide states with the choice of either providing a flat, federally backed $200 per-week increase in unemployment benefits or sufficient funds to replace two-thirds of prior income.

The $200 is a significant reduction from the $600 per-week increase provided under the current coronavirus relief law. Johnson tried to get unanimous consent to pass his bill earlier Thursday, but he faced a predictable objection from Schumer.

The New York Democrat instead tried to pass the nearly $3.5 trillion broader aid package that the House passed back in May on a nearly party-line vote. That measure would, among other things, renew the $600 added unemployment benefit through next January. Republicans objected.

Another GOP proposal, more generous than the Johnson-Braun offering, was formally unveiled Thursday by Sen. Mitt Romney, R-Utah, along with two Republican senators in hotly contested 2020 races: Susan Collins of Maine and Martha McSally of Arizona.

Romney’s plan would provide states with the option of switching to 80 percent wage replacement. States also could opt for a sliding benefit of an extra $500 increase each week in August, $400 each week in September and $300 each week in October.

That’s more generous than the proposal rolled out by GOP leaders earlier this week to provide a flat $200 per week benefit for two months while states work to set up a 70 percent wage replacement standard.

Cornyn said it was possible Romney’s proposal could also get a vote. But he said the shell was also a potential vehicle for broader pandemic relief legislation, if such a deal could be struck.

Floor theatrics

Earlier Thursday, senators were already sensing they’d be leaving Capitol Hill for the weekend without a deal. The floor theatrics were in full effect Thursday before they departed for their home states, many of them which are more ravaged by COVID-19 than the nation’s capital.

“This president has got to get away from the medical quackery that he spreads around on his Twitter account,” Minority Whip Richard J. Durbin said from the floor. “He’s got to stop looking at these medical gurus that he discovers in some weird corner of the internet, peddling their goods to the rest of America.”

Durbin also said that lawmakers need to reach an agreement before departing for August recess.

“I will just say flat out: There is no point to considering going home at the end of next week unless we have solved this problem, and there’s no excuse,” the Illinois Democrat said.

Although the $600 weekly federal supplement technically expires Friday, claimants actually stopped receiving their benefits this week already. That’s because states distribute unemployment insurance for weeks ending Saturday, or Sunday in the case of New York. Therefore, last week was actually the final week of eligibility for enhanced benefits.

Before senators began trickling out of town for the weekend Thursday afternoon, McSally went to the floor to try a last-ditch unanimous consent effort to renew the $600 benefit for seven days. Schumer blocked the move, saying “a one-week fix can’t be implemented in time and the senator knows that.”

McSally retorted that the only reason Schumer objected was that “it’s the minority leader who’s against this on his path to become the majority leader. And that’s unfortunate.”

Inside Elections with Nathan L. Gonzales rates McSally’s race “Tilt Democratic.”

Thom Tillis, R-N.C., also said he backed the one-week renewal. His race is rated a “Toss-up” by Inside Elections.

Schumer and Pelosi said such efforts were meaningless because state unemployment agencies couldn’t even get the benefit up and running again that quickly.

“What is a one-week extension good for?” Pelosi said after the late-night meeting. “It’s worthless.”

Lindsey McPherson and David Lerman contributed to this report.