Senate Majority Leader Mitch McConnell (R-Ky.) convened the bipartisan discussions on Friday morning, urging both sides to have a deal — or at least the framework of an agreement — in place by the end of the day so the Senate could vote on the package by Monday. But talks will now go into the weekend. And Republicans warned that they would begin drafting their own bills Saturday, even without a bipartisan accord.

“There’s still some significant outstanding issues, very significant to our side, that they haven’t agreed to,” Senate Minority Leader Chuck Schumer said.

Schumer said Friday evening that he was “hopeful” a deal can be reached but negotiators still had a long way to go.

Senate Finance Committee Chairman Chuck Grassley (R-Iowa), whose panel oversees a big portion of the economic-relief package, said there are “three or four [issues] that have to be worked out.”

Among the unresolved issues are increased unemployment insurance payments, significant financial assistance for hospitals and health-care providers to treat coronavirus victims, and a proposed “State Stabilization Fund,” which is intended to address billions of dollars in looming revenue shortfalls suffered by state governments during the emergency.

But Republicans believe that Democrats won’t block any rescue bill over fear of the potential political fallout.

“As I said, there’s been a lot of good conversations, a lot of substantial progress, but with the way the schedule is now accelerated in the Senate, the Senate needs to begin drafting legislative text, and they’ll turn to that next,” said White House Legislative Affairs Director Eric Ueland.

Ueland added that the White House and Senate Republicans “are very hopeful” that Democrats “won’t elect to grind it to a halt or gridlock it on the floor because a lot of improvements made in the legislation involve reflection of the concepts that they brought to Senate Republicans and us over the next several hours.”

McConnell’s proposed timetable for finishing work on what is likely to turn out to be the most expensive economic rescue package in American history sets an incredibly ambitious pace. Republicans and White House say there is an urgent need to address the growing public-health emergency, and McConnell is already preparing to take the procedural moves needed to make that happen.

The negotiations began Friday morning in the historic Hart 216 room, where Supreme Court nominations and crucial hearings often are held, and then shifted to the Finance Committee’s offices as four “task forces” and sub-groups met. Treasury Secretary Steven Mnuchin spent the day huddled with senators from both parties as they searched for an agreement. Mnuchin also had multiple phone conversations with Schumer and Speaker Nancy Pelosi (D-Calif.) to try to work through problems in the “Phase 3" package.

“I tasked these bipartisan teams to reach agreement by the end of the day today, tonight,” McConnell said. “We’ll need Saturday to be drafting what we’ve agreed to … We’ll need tomorrow for Legislative Counsel to draft the agreement. And as [Mnuchin] has indicated, it is important for us to be on the Senate floor and pass the measure by Monday.”

The four task forces — which covered distressed industries, small business, financial assistance to individual Americans and health care — took a “pause” in the middle of Friday afternoon while Republicans huddled for a policy lunch and Senate aides rushed to put the proposals into writing.

Yet it was clear by early evening that McConnell’s midnight deadline was going to be missed. Both sides said they would begin again early Saturday morning.

The high-level talks come a day after Senate Republicans introduced their $1 trillion stimulus package to save the U.S. economy by assisting individuals, small businesses and industries that have been hit hard by the pandemic.

But Senate Democrats argue the GOP proposal overall benefits businesses and industries while not doing enough for average Americans.

Schumer, who also spoke to President Donald Trump Friday morning, asked the president to use the Defense Production Act for more medical equipment, including ventilators, according to Schumer’s spokesperson.

During a sometimes angry 90-minute press conference at the White House, Trump said he had an “extremely good” conversation with the minority leader and expressed optimism about the “Phase 3” stimulus deal.

“We were working on various elements of the deal, and the Democrats are very much wanting something to happen, and the Republicans likewise are very much wanting something to happen. And I think it will,” Trump said at a daily press briefing of the White House coronavirus task force. He didn’t address the Defense Production Act.

Trump added that he also spoke at length with McConnell as well.

Among the key provisions of the Senate GOP plan is direct cash payments to individuals of up to $1,200 and families of up to $2,400, based on income. In addition to direct cash payments, the GOP stimulus plan gives small businesses $300 billion in federally guaranteed loans and $200 billion for loans for industries, including airlines.

The structure of the direct payments has emerged as a concern for some Republican members, in addition to Democrats. Sen. Lindsey Graham (R-S.C.) has panned the idea of direct cash payments broadly, while Sens. Josh Hawley (R-Mo.) and Mitt Romney (R-Utah) are calling for the package to be fixed, after expressing concern that its structure doesn’t sufficiently benefit lower income Americans. Hawley introduced an amendment Friday to help resolve the issue.

“Our goal is to create an income stream not just a one-time payment,” Graham said Friday. “The problem with direct cash is you’re giving it to the people who have got their salary, they don’t need extra money. There are people without money that need money.”

Senate Republican aides and White House officials are signaling they’re open to making changes during negotiations.

But Republican leaders also brought in Labor Secretary Eugene Scalia to counter the Democratic call for using the existing state-based unemployment insurance system to dole out money to those in need. Scalia argued in the closed-door sessions that some states’ unemployment systems aren’t capable of handling both an expected tidal wave of new unemployment filings by Americans who just lost their jobs while at the same time gearing up to send out millions of checks.

“The administration has expressed, based on some feedback they’re getting from states, that that would take a very long time,” said Senate Majority Whip John Thune (R-S.C.). “Again, we’re trying to do something that’s quick and gets an infusion of cash out there in a hurry, and the direct payments do that.”

There are also objections being raised to some of the industry specific bailout, as well as numerous business-related tax cuts offered by Senate Republicans. Democrats claim that the GOP bill is not “worker friendly,” and note that one of the provisions floated by Republicans would give a tax break to foreign subsidiaries of U.S. companies. “That is a complete non-starter on our side,” said Sen. Ron Wyden (Ore.), top Democrat on the Finance Committee.

And Trump himself said he wanted to make sure there was language in the Senate package preventing corporations from using federal aid for stock buybacks.

“We have some fundamental disagreements on some of the liquidity provisions,” said a Republican senator who spoke on the condition of anonymity. We’re trying to help not because we’re interested in helping business ... as much as we’re just trying to help keep the economy moving and keep people employed.”

In addition to Mnuchin, Scalia, and Ueland, administration officials participating Friday include former Council of Economic Advisers Chairman Kevin Hassett and National Economic Council Director Larry Kudlow.

“Very good attitude, the children are playing well,” Kudlow said when asked about the tenor of the discussions.

The Republican senators attending the talks are McConnell, Banking Committee Chair Mike Crapo (Idaho), Sen. Pat Toomey (Pa.), Finance Committee Chairman Chuck Grassley (Iowa), Sen. Rob Portman (Ohio), HELP Committee Chairman Lamar Alexander (Tenn.), Aging Committee Chairwoman Susan Collins (Maine), Small Business Committee Chairman Marco Rubio (R-Fla.), Senate Commerce Committee Chairman Roger Wicker (Miss.) and Thune.

Among the Senate Democrats participating are Schumer, Wyden, Commerce Committee Ranking Member Maria Cantwell (Wash.), Minority Whip Dick Durbin (Ill.), Small Business Committee Ranking Member Ben Cardin (Md.), Foreign Relations Committee Ranking Member Bob Menendez (N.J.), Sen. Jeanne Shaheen (N.H.) , Sen. Debbie Stabenow (Mich.) and Sen. Jack Reed (R.I.). HELP Committee Ranking Member Patty Murray participated by phone.

Lawmakers are trying to move as quickly as they can and are expected to work through the weekend. McConnell has vowed the Senate will not leave Washington until a deal is reached.

“There’s been some good constructive discussions about the issues,” Thune said. “We’re trying to narrow the list of the Democrat asks and the things Republicans want. We want feedback from the bill that we put out there ... We have about 12 hours to do it.”

Durbin, for his part, said Democrats “proposed a number of new issues that have not been raised by the Republican plan.” Democrats want hundreds of billions of dollars for hospital and health-care providers that the GOP proposal doesn’t presently include.

Schumer is closely consulting with Pelosi throughout the Senate negotiations. While Schumer is unlikely to agree to any major provision that Pelosi opposes, that doesn’t mean House Democrats can’t include additional initiatives when that chamber takes up the bill.

“At the speaker’s direction, House Majority committee staffs are working through Pelosi’s policy operation to weigh in through Schumer staff on key provisions House Democrats want added to the McConnell proposal,” said a senior Democratic aide.

McConnell, however, has refused to include Pelosi in the negotiations so far, despite pleas from both top Democrats to do so.

Heather Caygle and Quint Forgey contributed to this story.