WASHINGTON — President Donald Trump’s push for payroll tax cuts and other stimulus to help prop up markets hit hard by coronavirus fears faced a steep climb after getting a lukewarm reception from key Republican lawmakers Tuesday, worried about the proposal’s lack of detail.

“It wasn’t a specific proposal,” said South Dakota Sen. John Thune, the No. 2 Republican in the chamber, about Trump’s proposal. Officials, he said, still need to “put pencil to paper.”

“Ultimately you’re going to have to have Democrat buy-in,” the majority whip added.

Democrats — who control the House of Representatives — have largely given Trump’s proposals the cold shoulder.

Still, the president remained upbeat as he left Capitol Hill to head back to the White House after a working lunch with the Republican Senate caucus.

“There’s great unity within the Republican Party. And we’re working on a lot of different things,” he told reporters, while providing few specifics.

Trump also shrugged off GOP skepticism about another round of tax cuts, as the deficit balloons.

“Well, I was just with the Republican senators, and there was — they were just about all there, mostly all there — and there’s a great feeling about doing a lot of things,” he replied. “And that’s one of the things we talked about.”

Trump also hinted at possible aid for the coronavirus-battered airline and cruise ship industries during an event with health insurance executives on Tuesday.

The White House’s push for an economic stimulus package comes as officials push back against criticism the administration has mishandled the coronavirus outbreak — and seeks to calm worried markets that posted their biggest losses last week since the 2008 banking collapse.

During his Capitol Hill appearance, Trump for a second day attempted to assuage fears about the virus, which has left all of Italy under lockdown and several lawmakers — including incoming acting Chief of Staff Mark Meadows — under self-quarantine.

“It will go away, just stay calm. Be calm. It’s really working out. And a lot of good things are going to happen,” Trump said.

Senate Majority Leader Mitch McConnell said he was optimistic that Congress and the administration could work out a deal.

“I think the package needs to be negotiated … the way forward is the way we handled it last week. Come together, I’m confident the treasury secretary and the speaker can find a way forward,” he said, referring to Steven Mnuchin and House Speaker Nancy Pelosi (D-Calif) who met for about a half-hour.

But a deal appeared a long way off as top Democrats opened fire on Trump’s lightly sketched request for new tax cuts.

“You know what doesn’t help stop the spread of the coronavirus? More corporate tax cuts,” Senate Minority Leader Chuck Schumer (D-NY), told reporters, referring to reports that the president wants to help allies in the battered oil industry.

While the market rebounded by more than 1,160 points Tuesday, the president continued hammering Fed Chair Jay Powell over interest rates.

“Our pathetic, slow moving Federal Reserve, headed by Jay Powell, who raised rates too fast and lowered too late, should get our Fed Rate down to the levels of our competitor nations. They now have as much as a two point advantage, with even bigger currency help. Also, stimulate!” he tweeted. President Donald Trump went to Capitol Hill Tuesday to pitch his idea for payroll tax cuts and other economic stimulus to get the nation through the coronavirus scare, but even Republican senators said his ideas lacked the specifics they’d need to battle it out with Democrats over the proposal.

Trump, meanwhile, said he did not get tested despite rubbing shoulders with Republican Reps. Doug Collins of Georgia and Matt Gaetz of Florida — who were possibly exposed to the virus at the CPAC conference — because he had no symptoms and the White House physician saw no reason for him to be tested.

He also said he had no plans to fire anyone over the government’s handling of the outbreak — and insisted that the testing process was working well.

“The testing has gone very well. And when people need a test, they can get a test. When the professionals need a test, when they need tests for people, they can get the test. It’s gone really well,” he said.

Asked about reports that as many as 100 million Americans could be infected, he said the US was prepared.

“I’ve been briefed on every contingency you could possibly imagine. Many contingencies. A lot of positive. Different numbers, all different numbers, very large numbers, and some small numbers too,” Trump said.

The CDC said earlier in the day that fewer than 5,000 Americans had been tested for the virus.

Trump said earlier Tuesday that his administration was working closely to help the beleaguered airline and cruise ship industries, which have been battered by the coronavirus.

“We are working very closely with the cruise line industry, and … taking strong steps in terms of people going on and going off. But they are spending a lot of money and they are working very hard, and we’re going to be helping that industry,” the president said at the White House during a sitdown with top health insurance company execs.

“Likewise with the airline industry. They’re taking very, very strong steps for people coming into our country, even getting off the planes. So we are working very closely with them, we’re helping them. They’re two great industries and we’ll be helping them through this patch, and so far I think it’s been going very well,” he said