WASHINGTON (AP) — A bipartisan group of lawmakers unveiled a detailed COVID-19 aid proposal on Monday in hopes it would serve as a model for its battling leaders to follow as they try to negotiate a final agreement on a new round of virus relief.

The dozen or so lawmakers unveiled two bills. One is a $748 billion aid package containing money for struggling businesses, the unemployed, schools, and for vaccine distribution. The other bill proposes a $160 billion aid package for state and local governments that’s favored by Democrats and GOP-sought provisions shielding businesses from COVID-related lawsuits. But agreement proved impossible and most Democrats opposed a compromise on the liability issue forged by GOP Sen. Rob Portman of Ohio.

The path forward for their proposals — and for COVID-19 aid more generally — remains unclear. Parallel negotiations over virus relief and government funding are proceeding on the leadership level involving House Speaker Nancy Pelosi, D-Calif., and Treasury Secretary Steven Mnuchin. Senate Majority Leader Mitch McConnell, R-Ky., and that’s where any agreement is likely to be forged.

Speaker of the House Nancy Pelosi and Treasury Secretary Steven Mnuchin spoke later Monday evening in a 22 minute long phone call, Drew Hammill, Deputy Chief of Staff for Pelosi wrote on Twitter.

“Both the status of talks on COVID relief and remaining open items on the omnibus,” said Hammill. “The Speaker conveyed that the remaining open items on omnibus could be readily resolved and enlisted the Secretary’s help in the discussion of inadequate Davis-Bacon protections in the energy section and again raised the bipartisan support for inclusion of surprise billing.”

Hammill went on to explain in a tweet, “With regard to COVID, the Speaker reiterated Democrats’ concerns about the liability provisions, which remain an obstacle to securing state and local funding.”

He said both sides recognize the need to come to a “final agreement on both matters together and quickly this week, the Speaker and the Secretary discussed the urgency of the committees finishing their work as soon as possible.”

Outstanding issues in the leadership talks include a potential second round of direct payments to individuals, a plan for $300 bonus unemployment benefits, state and local aid, and the GOP-sought liability shield against COVID-19-related lawsuits.

Sen. Susan Collins, R-Maine, said she hoped that top Capitol Hill leaders and the administration will use the proposals as the basis for a COVID-relief package “that is urgently needed by our struggling families, our hard-hit small businesses, our stressed-out health care providers, our overwhelmed Postal Service, our challenged schools, and so many others.”

A key tradeoff involves aid to states and local governments, a top Pelosi priority, and the liability shield, a top demand of McConnell. The Kentucky Republican has suggested an all-or-nothing approach in which the fate of both ideas is linked to the other — either both are added or both are dropped. Pelosi is insisting, so far, that state and local aid be added, demanding that McConnell compromise on his pet provision. Agreement remains elusive.

But progress was being reported on another key front, too, as lawmakers cobbled together a year-end catchall funding package that will be the basis for the last significant legislation of the Trump presidency.

There’s a deadline on midnight Friday to deliver the completed package to President Donald Trump, which is when a partial government shutdown would arrive with the expiration of last week’s temporary funding bill. But there’s no guarantee that the massive year-end measure will be completed in time.

Meanwhile, negotiations on a $1.4 trillion catchall spending bill are “essentially finished,” said a congressional aide participating in the talks. While details are closely held, “the status quo is prevailing.” That means Trump would get another $1.4 billion or so for a final installment to continue construction of his long-sought U.S.-Mexico border wall.

Republicans have succeeded in killing a $12 billion plan to break last year’s budget mini-agreement by using accounting maneuvers to pad veterans health care funding to accommodate big cost increases from expanding access to health care services from private providers. Instead, a different set of moves is being employed to provide for equivalent spending increases for other domestic programs.

At issue are two long-delayed pillars of Capitol Hill’s agenda under divided government — COVID-19 relief and the annual appropriations process by which Congress passes day-to-day agency funding bills. Election-year politics and the maddening dysfunction of the Senate have stalled legislation on both topics for months.

The post-election lame-duck session is the last chance to wrap up the unfinished work this year, a goal of all involved, though they have been slow until now to forge the often-tricky compromises required to pull the measure together.

Pelosi and Mnuchin spoke Sunday, she has not thrown in the towel on her drive to obtain state and local aid, which was part of the almost $2 trillion CARES Act in March.

President-elect Joe Biden wants as much COVID relief as possible but has no direct influence on the negotiations. While he’ll empower Democrats after taking office next year, GOP leaders like McConnell are playing hardball and have forced Pelosi to scale back her demands. And while McConnell supported a $300 per week bonus unemployment benefit this summer, he’s pulled back after the November election.

No. 2 House Democrat Steny Hoyer of Maryland displayed flexibility in an appearance on CNN on Sunday that Republicans interpreted as a harbinger of further Democratic retreat.

“The legislative process is a give and take and the items that I just mentioned are absolutely critical to get done, and although I think state and local assistance is critically important, the others are critically important too,” Hoyer said.

“I would be shocked if we didn’t see something pretty concrete by at least Wednesday,” said Sen. John Cornyn, R-Texas. “Because we got to vote on this thing by Friday and get out of here.”

Also in the mix is a deal to curb “surprise medical bills,” the astonishingly high fees charged to patients with health insurance when they are treated by a doctor or hospital outside of their insurer’s provider network. It’s a particular problem for people getting emergency services and for patients undergoing complex surgeries where another specialist might have to be called in.

Although there’s agreement among most lawmakers and the White House that patients should not face thousands of dollars in unexpected bills, legislation has been slow to gel. It’s been blocked by a lobbying war between consumer groups and insurers on one side, and on the other, doctors and investors in medical practices. The potential compromise would ban surprise bills for emergency room visits and scheduled procedures, but McConnell has yet to endorse the agreement.