President Trump Donald John TrumpHR McMaster says president's policy to withdraw troops from Afghanistan is 'unwise' Cast of 'Parks and Rec' reunite for virtual town hall to address Wisconsin voters Biden says Trump should step down over coronavirus response MORE’s push to cut the payroll tax as part of an effort to revive the economy is facing steep headwinds on Capitol Hill.

Trump has spent days making the pitch publicly, as well as privately, as Washington is under growing pressure to try to shore up the stock market, which has plummeted this week over growing concerns about the growing coronavirus outbreak.

House Democrats are set to unveil an economic response package that does not include a payroll tax cut. Meanwhile, Senate reactions range from deep skepticism to, in some cases, outright opposition, raising questions about whether a plan could ever reach Trump’s desk.

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“I know that’s in the conversation … I would prefer they exercise other options before going down that path,” said Sen. John Thune John Randolph ThuneThe 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 Senate GOP eyes early exit MORE (S.D.), the No. 2 Republican senator, while caveating that it's “too early” to make decisions on legislation.

Sen. Mike Braun Michael BraunPessimism grows as hopes fade for coronavirus deal McConnell shores up GOP support for coronavirus package Patient Protection Pledge offers price transparency MORE (R-Ind.) predicted that a payroll tax cut would spark resistance not only from fiscal hawks but a broader swath of the Senate GOP caucus.

“I think there are going to be a lot of fiscal conservatives, and I think that’s going to go deeper into the conference than normal,” Braun said, asked about opposition to the idea. “My gut is there’s going to be folks not interested in doing it quickly.”

Asked if he was one of those who would be opposed to quickly passing a payroll tax cut, Braun added: “I would be one of them.”

The skepticism from Republicans comes after Trump met behind closed doors with GOP senators during a closed-door caucus lunch on Tuesday. During the powwow, the president stressed that he wanted a payroll tax cut until the end of the year. He also floated the idea of zeroing out the payroll tax altogether until after the Nov. 3 election.

Sen. Lindsey Graham Lindsey Olin GrahamThe Hill's Campaign Report: Arizona shifts towards Biden | Biden prepares for drive-in town hall | New Biden ad targets Latino voters Senate Democrats' campaign arm announces seven-figure investment to boost Graham challenger Graham: Comey to testify about FBI's Russia probe, Mueller declined invitation MORE (R-S.C.) described the reaction within the Senate GOP proposal as “mixed.”

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“I don't know if that's the best way to do it,” he said. “The president is pushing it.”

Congress last extended a payroll tax cut package in 2012 during the Obama administration.

“We are working out details right now, so I don’t want to quote any numbers ahead of time,” National Economic Council Director Larry Kudlow told reporters. “I think the outline of the thing is very important. The payroll tax holiday is probably the most important powerful piece of this.”

But a proposal is unlikely to garner similarly strong bipartisan support this time around.

Senate Democrats railed against a payroll tax during a press conference on Wednesday.

Sen. Ron Wyden Ronald (Ron) Lee WydenGOP senator blocks Schumer resolution aimed at Biden probe as tensions run high Republican Senators raise concerns over Oracle-TikTok deal Hillicon Valley: TikTok, Oracle seek Trump's approval as clock winds down | Hackers arrested for allegedly defacing U.S. websites after death of Iranian general | 400K people register to vote on Snapchat MORE (Ore.), the senior Democrat on the Finance Committee, called Trump’s payroll tax proposal a “huge mistake” that would “amount to hundreds of billions of dollars in tax cuts for big corporations.”

“What they want to do is hit Social Security like a wrecking ball with a massive tax cut for the country’s biggest corporations,” Wyden added. “We are going to oppose this with everything we have.”

“With respect to the Senate Finance Committee and our Democrats this will not happen. Period. Full Stop,” he added.

And House Majority Leader Steny Hoyer Steny Hamilton HoyerHouse Democrats postpone vote on marijuana decriminalization bill Democrats scramble on COVID-19 relief amid division, Trump surprise The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Md.) shot the idea down on Wednesday.

“I think it's a non-starter. The Republicans have expressed not much enthusiasm for that proposal either,” he said.

Some experts have criticized the idea of a payroll tax cut because it would not help workers who could be laid off as part of an economic downturn sparked by the coronavirus. Democrats, instead, are focusing on policy proposals like paid sick leave and bolstering unemployment insurance.

Sen. Chuck Grassley Charles (Chuck) Ernest GrassleySenate Republicans signal openness to working with Biden Senators offer disaster tax relief bill Trump spikes political football with return of Big Ten season MORE (R-Iowa), the chairman of the Finance Committee, acknowledged the likely opposition from Democrats on Wednesday, telling Bloomberg that the idea “does not have bipartisan support.”

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Grassley stressed during a pen-and-pad with reporters that he was not ruling out a payroll tax cut, or any other idea.

“It's just on the table, that's all there is,” he said.

But other GOP senators appeared lukewarm to the general idea, indicating that Trump could face an uphill lift to sell members of his own party on the proposal.

Sen. Ron Johnson Ronald (Ron) Harold JohnsonSecond GOP senator to quarantine after exposure to coronavirus GOP-led panel to hear from former official who said Burisma was not a factor in US policy The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump contradicts CDC director on vaccine, masks MORE (R-Wis.) said the “path of least resistance” would be the administration and states focusing on steps they can take unilaterally or using resources they already have, before trying to get something through Congress.

“The quickest way to get relief to American families is using existing authorities and existing funds,” Johnson said, asked if he supported a payroll tax cut. “Rather than trying to get something through this place.”

Asked if he could support a payroll tax cut, Sen. 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.), the chairman of the Appropriations Committee, said he wants to see what gets proposed because “here’s a lot of things bandied around.” Sen. John Cornyn John CornynAirline job cuts loom in battleground states Senate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll MORE (R-Texas) similarly kept his distance from the idea.

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“I think the details matter. I would be willing to consider it, but the details matter,” he added. “Not the least of which is how you're going to shore back up the Social Security trust fund, if you have a payroll tax holiday.”

Sen. Kevin Cramer Kevin John CramerOn Paycheck Protection Program, streamlined forgiveness is key McConnell shores up GOP support for coronavirus package Army Corps urges DOJ to settle case with ND over M DAPL damages MORE (R-N.D.) said he wasn’t on board with the idea yet, but didn’t rule out that the administration could win him over.

“I could be convinced to support it. ... I’d like to continue the discussion of whether we can combine it with other stimulus,” Cramer said. “The more I’ve heard about it, the warmer I am to it.”

Asked if he thought it could pass as a stand-alone, Cramer predicted that wouldn’t happen: “It really just seems unlikely.”

Niv Elis and Alexander Bolton contributed.