Senate Majority Leader Mitch McConnell and Speaker Nancy Pelosi have been in a standoff for months over coronavirus funding — but there were glimmers of hope late Wednesday that the chances for a deal may be improving.

Pelosi and Senate Minority Leader Chuck Schumer offered a secret proposal to McConnell and House Minority Leader Kevin McCarthy on Monday that sources said totaled around $1.3 trillion, but it went nowhere. In an effort to push things forward on Wednesday, the duo publicly urged McConnell to instead use a bipartisan Senate proposal released earlier this week as the basis for negotiations.

"While we made a new offer to Leader McConnell and Leader McCarthy on Monday, in the spirit of compromise we believe the bipartisan framework introduced by senators yesterday should be used as the basis for immediate bipartisan, bicameral negotiations," Pelosi and Schumer wrote.

"Of course, we and others will offer improvements, but the need to act is immediate and we believe that with good-faith negotiations we could come to an agreement."

McConnell's office did not immediately comment on the plan but his top GOP deputy, Senate Majority Whip John Thune (R-S.D.), told reporters the Democratic offer was a positive first step toward breaking the long running logjam. Democratic and Republican leaders have been at odds for months over the price tag of the next relief bill, with McConnell pushing a $500 billion proposal and Democrats demanding something in the ballpark of $2 trillion.

"They had this huge request, which was unreasonable. They've gotten reasonable and I think that could help us get to a solution," Thune told reporters Wednesday.

Lawmakers, who haven’t approved any substantially new aid since April, are under pressure to deliver relief as virus cases spike across the nation and the economy continues to falter. The bipartisan Senate plan released Tuesday totals $908 billion in funding, including $160 billion in state and local aid and $180 billion in additional unemployment insurance. But McConnell, so far, remains on his own path, with plans to revive and tweak his targeted package for a vote.

Thune suggested that congressional negotiators could "merge" the McConnell plan with the bipartisan Senate proposal to reach a deal in the coming days. But with just days before Congress is set to depart for the holidays, any coronavirus deal "is probably gonna ride on the spending bill," he conceded.

Democrats have dismissed the McConnell proposal as a partisan nonstarter, and even senior Republicans such as Sens. Lisa Murkowski (R-Alaska) and Susan Collins (R-Maine) pushed back, describing it as a messaging bill with little chance of becoming law.

“In light of the Covid crisis that confronts us, I am hopeful that members will come to grips with decision-making — that will be a compelling reason for them to do so and reach compromise,” House Majority Leader Steny Hoyer (D-Md.) told reporters Wednesday.

Hoyer talked to McConnell on Monday — with plans to chat again Wednesday — and said the two agree on the need to provide stimulus relief and clinch a deal this week, despite the long odds of doing so.

“[McConnell] and I both agree that it would be optimal, if in fact we get to an agreement by the end of this weekend, get that agreement put on paper and memorialized so that we can consider it as early as Wednesday or Thursday of next week,” Hoyer said. “I know that sounds very optimistic.”

Congress is known for pulling together major deals in the waning hours before a deadline — and this lame duck session likely won’t be different. But senior lawmakers have already started to discuss the possibility of staying in session for another week to wrap up spending talks, at the very least.

Senate Appropriations Chair Richard Shelby met with McConnell on Wednesday afternoon about government funding, stressing that “we’re close to closing a deal on the omnibus. We’re not there yet, but we’re close.”

“The question is, can we do it before the deadline? Hopefully, but probably not,” he said.

Earlier in the day, Shelby said, "I think it's where we're headed at the moment,” when asked about the need for a brief stopgap spending bill that would buy more time to close out omnibus talks before the holiday.

But appropriators see pandemic aid as an issue for leadership that isn’t slowing down progress on an omnibus, aides said Wednesday. House Appropriations Chair Nita Lowey and Shelby have already agreed on topline funding levels for all 12 bills that will comprise an omnibus package — a major step toward clinching a final deal that would boost agency budgets through the end of the fiscal year.

Lawmakers likely need to reach an agreement in the coming days, with text of the omnibus spending package finalized by early next week in order to give the House and Senate enough time to set the procedural gears in motion for passage in both chambers.

Still, snags have popped up in recent days. For example, Lowey and Shelby have so far agreed to classify billions of dollars in veterans’ health spending through the VA Mission Act — legislation that President Donald Trump himself has championed — as emergency spending not subject to overall funding limits.

Appropriators hope to preserve what small increases are allowed in fiscal 2021 non-defense spending and spread that money elsewhere, avoiding cuts to popular programs that would follow if they had to accommodate about $12.5 billion in veterans’ health cost increases as non-emergency spending.

Earlier this year, Shelby suggested that Trump had signed off that arrangement, which has temporarily ensnared appropriations talks in the past. But now there are questions as to whether the White House will support emergency spending for veterans’ health.

The White House and the Office of Management and Budget didn’t respond to a request for comment on Tuesday. Pelosi spoke to Mnuchin about government funding on Tuesday, saying she “laid out the bipartisan progress that Chairman Shelby and Chairwoman Lowey have made.”

“I relayed my hope that the Administration would support this bipartisan path,” Pelosi said in a statement after the call, although it’s unclear if the two discussed veterans’ health spending.

A GOP aide close to the talks said Senate appropriators aren’t interested in holding “veterans’ health care hostage” when it comes to an omnibus deal.

A number of other issues remain open, including federal funding for police departments and the usual sticking points like border wall funding and detention beds as perennial problems.

Senate Republicans have proposed $2 billion in border wall funding, while House Democrats haven’t offered any more cash. Such issues are usually some of the last to get resolved and appropriators are still hopeful about finding a middle ground, which might just mean maintaining the status quo.

“I think things are on track,” one House Democratic aide told POLITICO. “Everyone remains optimistic that this can be finished.”

Burgess Everett contributed to this report.