Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellMomentum growing among Republicans for Supreme Court vote before Election Day Trump expects to nominate woman to replace Ginsburg next week Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral MORE (R-Ky.) said Republicans will work out a deal among themselves on a third coronavirus funding package before negotiating with Democrats.

McConnell has established three working task forces with Senate Republicans to field ideas and work with the Treasury Department on the upcoming bill, which is expected to touch on workers, small businesses and industries affected by the pandemic.

"These task focus will be working with the Treasury Department and Secretary [Steven] Mnuchin and his team to see if we can reach a Republican consensus," McConnell said.

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"We are trying to reach an agreement among ourselves as to what Senate Republicans and the administration favor doing next," he added.

McConnell declined to say what the three areas for the task forces are or which GOP senators are involved in them.

But according to a GOP aide, the task forces align with McConnell's stated goals for subsequent legislation: getting money quickly to American families, helping small businesses and making sure they can "access liquidity."

The GOP senators directly involved also include key committee chairmen such as Senate Finance Committee Chairman Chuck Grassley Charles (Chuck) Ernest GrassleySenate Republicans face tough decision on replacing Ginsburg What Senate Republicans have said about election-year Supreme Court vacancies Biden says Ginsburg successor should be picked by candidate who wins on Nov. 3 MORE (R-Iowa), Senate Appropriations Committee Chairman Richard Shelby Richard Craig ShelbySenate GOP eyes early exit Dems discussing government funding bill into February GOP short of votes on Trump's controversial Fed pick MORE (R-Ala.) and Senate Health, Education, Labor and Pensions Committee Chairman Lamar Alexander Andrew (Lamar) Lamar AlexanderToobin: McConnell engaging in 'greatest act of hypocrisy in American political history' with Ginsburg replacement vote Chamber of Commerce endorses McSally for reelection Trump health officials grilled over reports of politics in COVID-19 response MORE (R-Tenn.).

"You can't have 53 people write the bill, right? So what I'm doing is picking out groups of people to deal with three separate categories. And then I've told everyone else that if they have a really good idea, I've told them how to funnel that idea into that particular task force," McConnell said when asked about the task forces.

The decision to get a Republican deal first is a U-turn from the second coronavirus package that was primarily negotiated by House Speaker Nancy Pelosi Nancy PelosiSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Trump is betting big on the suburbs, but his strategy is failing 'bigly' Trump orders flags at half-staff to honor 'trailblazer' Ginsburg MORE (D-Calif.) and Mnuchin.

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But the dynamic resulted in congressional Republicans largely being sidelined, and many GOP senators took issue with the deal.

The Senate is expected to pass the second coronavirus package without changes, but McConnell acknowledged that it has opposition from some GOP senators.

"My counsel to them is to gag and vote for it anyway," he told reporters after a closed-door lunch with his caucus and Mnuchin.

The administration and Mnuchin are pitching the third coronavirus package as a way for Republicans to fix or counteract things they don't like in the second bill. That proposal, according to GOP senators, could top $1 trillion.

While the past two coronavirus bills started in the House, Republicans say they expect the mammoth bill they will craft will start in the Senate.

"Clearly that will have to go in two steps. ... First, Senate Republicans and the administration are going to try to reach an agreement on what we think is best" for phase three, McConnell said.

Once they are able to do so, McConnell said that would be a "logical time to sit down and make a deal" with Democrats.

The plan immediately received pushback from Senate Minority Leader Charles Schumer Chuck SchumerVideo 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 Pelosi orders Capitol flags at half-staff to honor Ginsburg MORE (D-N.Y.), who argued that the negotiations should start with leadership in both parties and both chambers involved.

"The plan that Leader McConnell laid out will only delay things," Schumer said. "I believe the best way to get this going is in a bipartisan way from the outset."

Schumer is working on his own $750 billion proposal, though he appeared open to spending more. Schumer's proposal would put money "directly into hands of American people" and include funding for a laundry list of issues such as bolstering hospital capacity, providing help for small businesses and delaying payments on federal loans.

A timeline for the third coronavirus package remains unclear, though lawmakers say they are feeling pressure to act quickly.

"Phase three will be something that we work on [in the Senate]. We obviously have a lot of our members who have ideas, and then ... it takes 60 votes to do anything in the Senate, so this has to be in cooperation, this has to be bipartisan, but we think the elements of the deal can come together fairly quickly," 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 (R-S.D.), McConnell's No. 2, told reporters after the lunch.

The Senate was expected to be out of town this week. Now, McConnell is vowing he will keep the Senate in session until the third coronavirus> package is passed.

"I cannot predict how long we will be here, but we will be here as long as it takes," he said.

Mike Lillis contributed