Whether or not Congress can agree on a coronavirus economic stimulus package will come down to two Washington players who know one another well.

Donald Trump told Republican senators he has put Treasury Secretary Steven Mnuchin in charge of negotiating such a package with lawmakers, a role he carried out successfully last year when he worked out a bipartisan spending deal with House Democrats.

Following the luncheon meeting with Mr Trump, Senate Minority Leader Mitch McConnell told reporters the Treasury secretary will be negotiating directly with Speaker Nancy Pelosi, the top Democrat across the Capitol with whom he worked closely on that spending pact.

"I think that Secretary Mnuchin will have ball control for the administration," Mr McConnell said. "And I expect that will speak for us, as well."

"We're hoping he and the speaker can pull this together so that we end up not playing partisan games," he said. "That's what I'm hoping to see, and hoping to see pretty soon."

A White House official said there is no date by which Mr Trump wants Congress to strike a deal and send him a package. But the official said the working relationship between the Treasury boss and speaker is there from their negotiations last year so they should trust one another as talks begin.

The White House is pushing a multi-faceted package that would include a payroll tax cut, assistance for hourly workers who might be stripped of pay if they get sick, federal loans for small business, and tax relief for affected industries like tourism, airlines and cruise lines.

As those talks commence, Mr Trump and Mr McConnell have some work to do. With their fellow Republicans.

"I don't know how I feel it," Senator Lindsey Graham of South Carolina said Tuesday of the payroll tax cut idea. "I'll think about it. I'll be open-minded to it."

And Senator John Kennedy of Louisiana has said he is not interested in approving a series of "bailouts" for companies and individuals.

Democrats do not sound hopeful that Mr Trump can help bring about a deal -- or that he wants to.

"We are very worried about the president's incompetence and lack of focus on fighting the spread of this virus," Senate Minority Leader Chuck Schumer said. "We believe that his lack of focus is hamstringing efforts to fight this virus."

Mr Schumer touted a Democratic-crafted stimulus proposal that has been widely rejected by Republicans over cost and other concerns.