Congressional leaders and the White House have an agreement in principle on a nearly $500 billion coronavirus relief package and are now working through the final details, Speaker Nancy Pelosi said Monday night.

“We have, I believe, come to terms on the principles of the legislation, which is a good thing. But then it’s always in the fine print, so now we’re down to the fine print,” Pelosi said on CNN.

While the California Democrat said she was “very optimistic” that the Senate could vote as early as Tuesday, several sources familiar with the talks who were not authorized to speak publicly said a final deal was unlikely until the wee hours of the morning at the earliest.

House Majority Leader Steny H. Hoyer updated lawmakers late Monday that the earliest that chamber would vote on the package is Thursday. Democratic leaders plan to call members back to Washington for a recorded vote due to likely objections to passing the measure by unanimous consent.

As talks dragged on, the broad outlines of the deal appeared set. The latest aid package in response to the global pandemic is likely to include an additional $310 billion for the so-called Paycheck Protection Program that provides small businesses with forgivable loans to keep employees on the payroll.

Negotiators have also agreed to $75 billion for hospitals, Treasury Secretary Steven Mnuchin and others have said, which is short of what Democrats sought.

At the White House, President Donald Trump was bullish about a deal and noted “tremendous progress had been made” without giving specifics. Vice President Mike Pence said some $25 billion would be available for coronavirus testing, which he urged would include funding for contact tracing.

The Senate met for a brief session Monday without taking action on the new legislation. The chamber is now expected to come back into session Tuesday at 4 p.m. to try to pass the bill, assuming the deal is in legislative form by then.

Senate Majority Leader Mitch McConnell, R-Ky., blamed the delay on Democrats as he announced Tuesday’s session.

Senate Minority Leader Charles E. Schumer tweeted shortly after McConnell’s remarks that Democrats were fighting for $30 billion to fund a comprehensive national COVID-19 testing strategy.

That’s slightly more than the $25 billion that Republicans said they’d agreed to, and GOP leaders also took issue with the nationwide scope of the program.

Democrats also continued to push for aid to state and local governments, which Trump said he does not support for the current “interim” measure focused on small businesses and health care.

Progressives not happy

While party leaders and Mnuchin continue to hash out the package’s finer points, progressive House Democrats panned the evolving bill on Monday. They criticized both the secretive process as well as reports of what’s been agreed to as insufficient to meet their constituents’ needs.

“Incrementalism is not helpful in this moment,” Rep. Alexandria Ocasio-Cortez, D-N.Y., said on a call with reporters.

“I would be amenable to accepting this kind of logic if Congress actually was in session and convening,” she added. “But if we’re going to say that this new bill is going to give us $5 and then Congress is going to peace out for another monthlong recess, I’m here to say that that’s not going to help our communities.”

[Obama small-business chief says Democrats should act now on loan funds]

Congressional Progressive Caucus co-Chairwoman Pramila Jayapal, D-Wash., said that left-leaning lawmakers had reservations based on what had been reported and would continue to try to influence the direction of the package.

“It’s going to be very difficult to support a package that doesn’t have some of the desperate relief that we need for state and local governments, for people,” Jayapal said.

The day began with the House’s top Republican blaming Democrats for the hold up, despite general bipartisan agreement on how much money should be allocated for aid to small businesses and health care providers and expanded testing capacity.

“We could have been done yesterday, but the Democrats continue to hold up, even though we have agreed to all the numbers,” House Minority Leader Kevin McCarthy said on Fox News.

National Economic Council Director Larry Kudlow cast doubt on whether the additional round of funding for the PPP would be enough, raising the prospect of even more in the future.

“The first [round] went like hotcakes. So the second one could go like hotcakes too,” Kudlow said.

The first round of PPP money, passed as part of a roughly $2 trillion economic relief package last month, ran out last week. Democrats rejected the administration and Republicans’ request for a stand-alone bill to infuse an additional $251 billion into the program, saying they wanted to ensure that smaller businesses without traditional lending relationships could access the money.

Despite the holdup in negotiations, Senate Small Business Chairman Marco Rubio, R-Fla., said Monday on CNBC that he was pleased with the outlines of the emerging deal.

However, he cautioned that it might take time for the SBA to get its systems updated to distribute loan funds through smaller financial institutions with less than $10 billion in assets, which the emerging aid bill would set aside money for.

“What I’m asking them to do is to start doing this now — not to wait until Thursday or Wednesday when this passes,” Rubio said.

Paul M. Krawzak and Doug Sword contributed to this report.