Top Republican senators are warning they oppose including a payroll tax cut in the next coronavirus relief bill, even though it's a top priority for President Trump.

Senate Finance Committee Chairman Chuck Grassley (R-Iowa) warned on Monday that he believes the move would create a public relations headache for Republicans.

"Go to the fact that Social Security people think we're raiding the Social Security fund. And we are raiding it, but we have always put in general fund revenue in it so it is made whole. But that creates — it might create political problems — but it creates a public relations problem," Grassley told reporters on Monday.

Asked about including a payroll tax cut, Sen. John Thune (S.D.), the No. 2 Senate Republican, told The Hill it would depend on where the “consensus” is, but that he did not personally support a payroll tax cut.

“I’m not a fan of that. I’ve made that pretty clear,” he said.

Sen. John Cornyn (R-Texas), an adviser to Senate Majority Leader Mitch McConnell (R-Ky.), also warned a it would be "problematic."

"I think it's problematic because obviously the trust funds for Social Security and Medicare are already on their way to insolvency. ... I'm not a fan," Cornyn said.

The pushback from Republican senators comes as GOP leadership and the administration have spent two weeks swapping ideas about what to include in the next coronavirus proposal. Treasury Secretary Steven Mnuchin and White House chief of staff Mark Meadows are expected to meet with Republican senators on Tuesday to brief them.

Trump touted the payroll tax cut during a meeting with GOP leadership, Meadows and Mnuchin on Monday, telling reporters that it was under discussion.

"I think it's a very important thing. ... I think it's an incentive for companies to hire their workers back. ... A payroll tax cut to me is very important," the president told reporters.

House Minority Leader Kevin McCarthy (R-Calif.) — who took part in the White House meeting — told reporters afterward that a payroll tax cut was expected to be in the Republican legislation.

McConnell sidestepped a question on Monday about whether it would be in the bill. He indicated over the two-week break that Republicans were looking at another round of stimulus checks but with a lower income ceiling for qualifying.

The CARES Act in March allowed individuals who made up to $75,000 a year to get a one-time payment of $1,200; McConnell has indicated lawmakers could lower that cap to people who earn roughly $40,000.

The administration has repeatedly pushed for a payroll tax cut to be included in coronavirus relief packages. But the effort has garnered pushback from both Republicans and Democrats, who warn that it won't stimulate an economy that has been battered by businesses that were closed or scaled back due to the spread of the coronavirus.

Grassley on Monday said he thought a direct check would have a bigger impact on Americans.

"I think when a person has a check in his hand, X number of dollars .... I think that is going to do more economic good than if we dribble out $30 every paycheck because people are going to notice it," he said.

He added that if Republicans were going to stick to their topline of roughly $1 trillion, which Mnuchin said he viewed as a starting point, he did not think both direct checks and a payroll tax cut could be included.

"I don't think you can fit them both in," Grassley said.

— Updated at 4:58 p.m.