President Trump on Thursday sought to blame Democrats after Senate Republicans rejected a payroll-tax cut in the coronavirus relief package that they're crafting with the White House.

"The Democrats have stated strongly that they won’t approve a Payroll Tax Cut (too bad!)," Trump tweeted. "It would be great for workers. The Republicans, therefore, didn’t want to ask for it. Dems, as usual, are hurting the working men and women of our Country!"

Trump has been pushing for a payroll-tax cut throughout the coronavirus pandemic, and said in a recent Fox News interview that he might not sign a relief package that doesn't include one. He argued that such a tax cut would provide savings to workers and encourage businesses to hire and retain employees.

The White House and congressional Republicans have been working on a proposal that would lay out their priorities before negotiations with Democrats. Treasury Secretary Steven Mnuchin, White House chief of staff Mark Meadows and House Minority Leader Kevin McCarthy (R-Calif.) indicated as recently as Monday that a payroll-tax cut would be in the forthcoming legislation.

But few Republican lawmakers supported the idea. They raised concerns about such a cut's impact on Social Security, and said they preferred a second round of direct payments.

"My sense is ... there’s not much, I would say, support for the payroll-tax cut," Sen. John Thune (S.D.), the second highest ranking GOP senator, said Wednesday.

Mnuchin on Thursday said that while there won't be a payroll-tax cut in Senate Republicans' forthcoming proposal, the idea could be a part of a subsequent coronavirus bill.

He said the GOP proposal would include a second round of direct payments that resemble the first round mandated by the $2.2 trillion CARES Act in late March when Congress provided for payments of $1,200 per adult and $500 per child for individuals with incomes of up to $75,000 and married couples with incomes of up to $150,000. The payment amounts phased out for people with income above those thresholds. 

Mnuchin argued Thursday that Americans would get more money faster through additional direct payments.

"One of the issues I think you know about the payroll-tax cut is, people get that money over time, so the president's preference is to make sure that we send out direct payments quickly, so that in August, people get more money," Mnuchin said on CNBC.

Many economists across the ideological spectrum argued that a payroll-tax cut wasn't the best way to provide financial relief to Americans, noting it wouldn't help people who are unemployed.

Congressional Democrats are also opposed to a payroll-tax cut; House Democrats did not include one in the $3 trillion coronavirus relief package they passed in May.

Jordain Carney contributed.