CNN  — 

A deal on a long-awaited rescue package to deliver pandemic aid remained elusive on Saturday as congressional leaders struggled to reach agreement amid a contentious dispute over the role of the Federal Reserve to intervene in the US economy.

Talks were expected to continue late into Saturday night as the two sides traded a flurry of proposals to resolve a disagreement over the central bank’s emergency lending authority – while the fate of the $900 billion deal, and whether one can be approved before government funding expires Sunday night, hangs in the balance.

With Americans eager for relief, impatience is growing in the ranks as both sides recognize a deal must be reached Sunday or the talks could collapse completely.

Sen. Chris Coons, a Delaware Democrat, said that a deal will either be reached Sunday on a compromise, or one side needs to make a “hard decision” about how to proceed.

“My hunch is what will happen tonight is repeated good faith efforts at language, and clarifying whether there is or isn’t something we can do to resolve this – and if not, a hard decision by one party or the other,” Coons said Saturday night. “Because this cannot go on.”

Both sides continue to exchange proposals over the biggest sticking point: How to rein in the emergency lending authority of the Federal Reserve.

Republicans argue that the emergency lending program created under the March CARES law needs to be wound down as envisioned by that law, saying leaving it open would amount to a slush fund for the incoming Biden administration.

But Democrats argue that the authority is essential to continue to prop up the economy and say that the provision to wind it down – pushed chiefly by GOP Sen. Pat Toomey of Pennsylvania – would tie the hands of President-elect Joe Biden’s team.

That dispute has created a narrow focus in the effort to lock down an agreement on a sweeping relief package.

Senate Minority Leader Chuck Schumer is engaged in talks with Toomey, and other Democrats are also taking part in the talks.

Sen. Kyrsten Sinema, an Arizona Democrat, met privately with Toomey and the two have discussed how to pare back Toomey’s proposal. The discussions led to further exchanges with Senate Majority Leader Mitch McConnell and other top Republicans to see if they can get a deal.

Leaving the Senate floor on Saturday, Sen. Bill Cassidy, a Louisiana Republican, said he thinks they will be able to get a deal.

“I think they’re going to resolve it,” Cassidy said, with a “more narrow focus.”

Schumer indicated on a call with Senate Democrats that if a deal is reached, a vote could happen in the Senate on Sunday night or Monday – but that would take consent of all 100 senators to allow that vote to happen.

Government funding is on track to expire on Sunday night, leaving lawmakers up against the clock.

Hill leaders had hoped to reach a deal by Saturday night to move an agreement to the House floor as soon as Sunday, but that schedule remains ambitious at best.

Senate Majority Whip John Thune warned on Saturday that the effort to finalize a deal could spill over into Monday.

“I’m still somewhat hopeful we could wrap this up if the House moves quickly and we got it, take it up, and do it tomorrow night, but I would say it’s also very possible that it rolls into Monday,” he said.

Toomey on Saturday signaled he thinks they’ll be able to reach an agreement on the controversial provision that’s held up relief talks, saying, “I think we should be able to get a deal done.”

But he added, “I don’t know what the timeframe of it is.”

Throughout the day, however, the two sides had appeared to be dug in over the issue.

Treasury Secretary Steven Mnuchin told GOP senators on a conference call that they still have not resolved the fight over whether to pare back the emergency lending programs of the Federal Reserve, according to a source on the call.

On a caucus call, Pelosi told Democrats that the main obstacle is the language pushed by Toomey to rein in the Federal Reserve’s emergency lending authority. She said there are other outstanding issues but that remains the biggest one, a source familiar with the call told CNN.

Pelosi said when she arrived at the Capitol on Saturday that “the plan” was to arrive at a deal today, but first they need to resolve the “significant difference” over the Federal Reserve funding issues.

“We had this big issue, a last, kind of, minute thing with Mr. Toomey. And that has to be resolved. And then everything will fall into place. But that’s the big thing,” she said.

Schumer similarly zeroed in on the dispute in remarks on the Senate floor Saturday, calling it the “number one outstanding issue” to securing a deal.

Asked for an update on talks earlier in the day, Durbin replied simply, “Toomey, Toomey, Toomey.”

The proposal, Schumer said, “is not about Covid or helping the American people. It’s about tying the hands of the next Treasury secretary and the next Fed chairman in a true emergency.”

McConnell said Saturday that congressional leaders “need to conclude our talks, draft legislation and land this plane.”

McConnell warned, “There’s a kind of gravitational pull here in Congress, where unless we’re careful any major negotiation can easily slide into an unending catalogue of disagreements.”

On a conference call with GOP senators, the Kentucky Republican noted that a dozen GOP senators have left town even though there are a number of votes lined up Saturday on approving nominations, according to two sources familiar. McConnell thanked the members who stayed in town.

The absent senators would need to return if there’s a vote Sunday on a relief package, but if there’s an attendance problem, a vote could potentially be delayed until Monday.

Hill leaders are facing growing pressure to lock down a deal as lawmakers remain in Washington this weekend and are now up against another rapidly-approaching deadline after a government shutdown was narrowly averted on Friday evening when the House and Senate approved a two-day extension of government funding.

Leadership is planning to pass a stimulus deal alongside a $1.4 trillion government funding package for a new fiscal year, tying the two issues together.

But in addition to the dispute over the Federal reserve, a series of other outstanding policy disputes has created last-minute holdups that lawmakers belief can be bridged. One of them is on education funding.

Currently in the emerging deal, there’s more than $80 billion for schools and education providers. Republicans are pushing for $5 billion of that to go to private schools. Democrats are trying to cut that to $2.5 billion.

With the clock ticking, rank-and-file members have become increasingly frustrated with the process, after leaders have signaled for days in a row that a deal is imminent, and with how little information has been released publicly about the details of such a significant bill that they expect to vote on soon.

Asked if leadership is getting closer to a relief deal, McConnell told reporters Friday evening, “Yeah, we’ve been close for a while now and we still are.”

House Majority Leader Steny Hoyer announced on Friday that the next votes in the House would not occur before 1 p.m. E.T. on Sunday, meaning that lawmakers will be once again backed up against a government funding deadline.

“We are hopeful they will reach agreement in the near future, they have not reached one yet, there are still some significant issues outstanding,” Hoyer said of the current status of talks.

This story has been updated to reflect additional developments Saturday.

CNN’s Ted Barrett, Ali Zaslav, Suzanne Malveaux and Kristin Wilson contributed to this report.