Senators are racing the clock as they try to clinch a deal on a massive stimulus package to address fallout from the coronavirus outbreak rattling the nation.

The Senate met for a rare weekend session on Saturday as lawmakers attempt to hammer out an agreement on a bill that is expected to cost at least $1 trillion — and potentially hundreds of billions of dollars more.

Though the Senate went out of session around 4 p.m., leadership, administration officials and key senators remain locked in closed-door negotiations as they try to finalize the deal and start drafting text of the mammoth bill.

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Sen. John Thune John Randolph ThuneWhat Senate Republicans have said about election-year Supreme Court vacancies The Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump contradicts CDC director on vaccine, masks MORE (S.D.), the No. 2 Senate Republican, said there was an agreement on the "general contours" of the package but that they were still working on "plugging in some of the policy" and numbers.

"I mean, there are some loose ends, and there are some policy pieces that still haven't been decided on," he added, saying that there is "general agreement" on the "major categories."

The hours of negotiations came after Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellOcasio-Cortez to voters: Tell McConnell 'he is playing with fire' with Ginsburg's seat McConnell locks down key GOP votes in Supreme Court fight Video shows NYC subway station renamed after Ruth Bader Ginsburg MORE (R-Ky.) had set a midnight Friday deadline for Congress and the White House to reach a deal "in principle" — a tall task for bipartisan negotiations that started in earnest earlier Friday morning.

The negotiations were then given a 5 p.m. deadline for Saturday, which passed without the announcement of a deal "in principle."

Eric Ueland, the director of legislative affairs for the White House, said that even if negotiators aren't able to lock down every detail, they had to start drafting legislative text, potentially bracketing the issues that are not yet agreed to.

"Again, we're working against a very tight deadline. ... The need for drafting legislation is pretty significant now, and the expectation is even if we can't get to an agreement on every piece and part here in the next few hours that the legislative drafters will go ahead and move on to writing legislation," he said.

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Sen. Chuck Grassley Charles (Chuck) Ernest GrassleyGOP set to release controversial Biden report McConnell locks down key GOP votes in Supreme Court fight Senate Republicans face tough decision on replacing Ginsburg MORE (R-Iowa) said the holdup on the deal was due to efforts to expand the package.

"The only thing is, when you keep adding at the last, within the last hour, or a couple things, as an example, then you have to go back and check on it. ... We've got a deadline," he told reporters.

The prospect that they might not be able to reach a deal "in principle" on Saturday comes even as top members of leadership appeared upbeat about their chances to get a deal.

Senate Majority Leader Mitch McConnell (R-Ky.) said early Saturday afternoon that groups were making "important progress," though a deal was not yet finalized.

"Both sides ... are continuing to work towards a bipartisan agreement on major legislation," he said.

McConnell told reporters on his way into a caucus lunch that talks were getting "closer and closer," adding, "Clearly, we’re going to get there.”

Senate Minority Leader Charles Schumer Chuck SchumerRepublican senator says plans to confirm justice before election 'completely consistent with the precedent' Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral Graham signals support for confirming a Supreme Court nominee this year MORE (D-N.Y.) said he had a "very good" and "very detailed" call with Treasury Secretary Steven Mnuchin Steven Terner MnuchinLawmakers fear voter backlash over failure to reach COVID-19 relief deal United Airlines, unions call for six-month extension of government aid House Democrats plan to unveil bill next week to avert shutdown MORE on Saturday. He started to say the discussion was "wonderful" before stopping himself.

"We discussed many of the outstanding issues, and we are making very good progress," Schumer said.

The Senate will hold its first procedural vote related to the stimulus package on Sunday at 3 p.m. The later time could give those involved more time to negotiate or finish drafting legislation, which senators have said they want to see before the initial vote.

Congress is under intense pressure to act quickly as the coronavirus spreads across the country and rocks the economy. There are now more than 24,000 cases and at least 285 deaths in the U.S., according to data from Johns Hopkins University. The economy, meanwhile, has cratered, with the Dow Jones Industrial Average dropping 9,000 points in the past month.

Lawmakers, their staff and top administration officials spent roughly 12 hours on Friday behind closed doors as they tried to get an agreement on the broad contours of the trillion-dollar stimulus package.

Sen. Ron Wyden Ronald (Ron) Lee WydenGOP set to release controversial Biden report Democrats fear Russia interference could spoil bid to retake Senate GOP senator blocks Schumer resolution aimed at Biden probe as tensions run high MORE (D-Ore.) told reporters on Saturday that he was preparing to work through the night, indicating a second long day of negotiations. He and Grassley began their first meeting around 10:30 a.m.

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Underscoring the frequency of the behind-the-scenes talks, Mnuchin told reporters on Saturday that he had spoken with President Trump Donald John TrumpBiden leads Trump by 36 points nationally among Latinos: poll Trump dismisses climate change role in fires, says Newsom needs to manage forest better Jimmy Kimmel hits Trump for rallies while hosting Emmy Awards MORE, Vice President Pence, McConnell and Schumer. He noted that House Speaker Nancy Pelosi Nancy PelosiAs families deal with coronavirus, new federal dollars should follow the student Sunday shows - Ruth Bader Ginsburg's death dominates Hypocrisy rules on both sides over replacing Justice Ginsburg MORE (D-Calif.) was at the moment on a plane but that he would speak with her later Saturday.

The talks are focused on four areas of an agreement: tax, health care, small businesses and impacted industries such as airlines.

Negotiators have suggested that they are closer to a deal, including moving toward resolving key sticking points such as a GOP proposal to send individuals a one-time check and a Democratic demand to expand unemployment insurance ahead of an expected major spike in jobless claims.

Ueland told reporters that “tremendous” progress had been made on the debate over unemployment and that there was bipartisan support for keeping the rebate checks in the final agreement.

“Nothing is agreed until everything is agreed to,” Ueland said, adding that “we're very gratified to hear ... bipartisan interest or some consensus that we need to act and provide direct relief.”

Thune told reporters on Saturday that Democrats will "get what they want" on unemployment insurance, a significant concession given that it was viewed as a top priority. Among other things, Schumer has specifically asked for six weeks with 100 percent of wages.

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A GOP senator added that they did not see the unemployment debate as a major sticking point at this time.

The sign of progress comes as the idea of rebate checks has emerged as a primary hurdle to getting an agreement.

The original Senate GOP plan would have provided a check of $1,200 to individuals who make up to $75,000 per year. The amount would have been scaled back until it hit an income level of $99,000 per year, where it would have phased out completely.

But some Senate Republicans raised concerns about the provision because it would have resulted in Americans with little or no tax liability getting a significantly smaller check — $600. Democrats also pushed back, arguing that unemployment insurance must be expanded to provide stability beyond a one-time payment.

The forthcoming deal is also expected to include money for stabilization funds, which states could fall back on if their economies worsen due to the coronavirus. The initial GOP plan that had included $300 billion for small businesses is expected to be ratcheted up to $350 billion.

The agreements on key provisions of the package comes after Schumer told reporters early Friday night that there were “significant issues” on the table, including the state money, but he hoped that a deal could be reached on Saturday.

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"I think we're making good progress, but I think it's a big, complicated, huge bill," he said. "I would hope we could come to agreements tomorrow."

The GOP leader and the White House both want to pass the agreement on Monday. McConnell would need cooperation from all 100 senators to move that quickly; otherwise, the bill could get dragged out until late into the week.

Sen. Pat Toomey Patrick (Pat) Joseph ToomeyAppeals court rules NSA's bulk phone data collection illegal Dunford withdraws from consideration to chair coronavirus oversight panel GOP senators push for quick, partial reopening of economy MORE (R-Pa.) added that there was an “urgency” for Congress to act.

“I think it’s likely that there will be a vote early next week. ... The leader has said it’s going to be Monday,” Toomey told CNBC, adding that lawmakers were under “pressure” to be ready by early next week.

No senators have said they would slow down the stimulus package. But the GOP leader had to cut deals with members of his own caucus on the previous two stimulus packages in order to let them skip over procedural hurdles.

Sen. Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (R-Ky.) forced amendment votes on the two previous coronavirus packages, putting him as a potential early hurdle for McConnell.

The GOP senator announced on Friday that he would introduce his own coronavirus bill that includes a 60-day payroll tax holiday and would replace paid sick leave with expanded unemployment insurance.

“The national emergency we face may be new, but the answers out of Washington have so far been the same: more spending, more debt, and more mandates on the American people,” Paul said.

If senators aren’t able to finalize a deal, Ueland said staffers had to begin drafting legislative text either way in order to meet McConnell’s deadline.

But Democrats were deeply critical of the Senate GOP proposal, signaling that it likely would not pass the Senate as originally drafted. Pelosi also wrote in a letter to colleagues on Friday night that the GOP plan “as written” is a “non-starter.”

Rep. Hakeem Jeffries Hakeem Sekou JeffriesPelosi: House will stay in session until agreement is reached on coronavirus relief Races heat up for House leadership posts Postmaster general earned millions from company with ties to Postal Service: report MORE (N.Y.), chairman of the House Democratic Caucus, said House Democrats, who are currently compiling their own stimulus proposals, will be pushing for "a bottom-up approach" featuring more funding for programs designed to help students, seniors, small businesses, working-class families, and those facing eviction and foreclosure.

It "will be wide-ranging and extraordinary because we're dealing with an extraordinary threat," he said.

Alexander Bolton and Mike Lillis contributed.

Updated 5:41 p.m.