Senate Majority Leader Mitch McConnell (R-Ky.) leaves a Republican luncheon on Tuesday. (Jacquelyn Martin / Associated Press)

Senate Republicans on Tuesday said they would include a new round of coronavirus stimulus payments in the upcoming pandemic relief bill, dramatically increasingly the likelihood that more checks will go out to help Americans combat the economic effects of the COVID-19 outbreak. Democrats had previously endorsed the idea.

“We want another round of direct payments to help American families keep driving our national comeback,” Senate Majority Leader Mitch McConnell (R-Ky.) said.

Republicans have not identified how much the payments should be or who should be eligible to receive them. They plan to release legislation in the coming days.

In a House bill passed in May, Democrats called for $1,200 payments to adults and $1,200-per-dependent for up to three children, phasing out for individuals with taxable incomes above $75,000 a year and couples above $150,000.

The support for a new stimulus payment marked a thin area of agreement in the negotiations between the White House and Republicans, and Democrats on Capitol Hill.

But even as negotiations got underway in earnest on Tuesday, both McConnell and House Speaker Nancy Pelosi (D-San Francisco) separately indicated that an agreement by the end of next week — when some of the relief funding approved by Congress in March begins to expire — was unlikely.

So far, Trump administration officials have held separate meetings with Republicans and Democrats. Republican and Democratic lawmakers have not begun direct talks, a sign of a slow start.

McConnell hopes to have obtained “fairly significant support” among Republicans before he begins talking with Democrats.

White House Chief of Staff Mark Meadows told reporters on Capitol Hill that “we’re very early on in the negotiations and the discussions. … To put it in a football term, we’re on our own 20 yard line.”

He met with Pelosi and Senate Minority Leader Charles E. Schumer (D-N.Y.) in Pelosi’s office Tuesday, but they emerged with no public agreements. Meadows said they were all waiting on Senate Republicans to put forward a bill. Democrats chided the GOP for so far being unable to even agree among themselves on a plan.

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But some areas of agreement are becoming clear.

There is support for continuing the enhanced unemployment payments that began earlier this year and are due to expire at the end of the month. The $600 payment, however, is expected to be whittled down.

Republicans are furious that people can receive more on unemployment than they did while working, and are determined to ensure that they don’t set up the same system moving forward.

Sen. Charles E. Grassley (R-Iowa), chairman of the Senate Finance Committee, cited a local employer with 250 employees who the employer said refused to go back to work because they had the enhanced unemployment payment. “So there’s a real problem we’ve got to work with,” Grassley said.

The Trump administration prefers an enhanced payment below about $300, according to an administration aide.

House Democrats are open to reducing the $600 or perhaps granting it to people deemed to be most in need. Any additional income qualifications, however, could slow down how quickly the money could move, reducing its effectiveness.

The dollar amount is “going to be a subject of discussion,” said House Majority Leader Steny Hoyer (D-Md.). “It is not irrational to talk about making sure the neediest are taken care of, either first or maybe only.”

In addition, both Democrats and Treasury Secretary Steven Mnuchin have expressed support for tax credits for employers who bring employees back to work.

Another area of agreement, among lawmakers on Capitol Hill at least, is opposition to President Trump’s plan to cut payroll taxes. Democrats and many Republicans say the idea is dead on arrival because it doesn’t actually help anyone who is not getting a paycheck. The proposal has support from only a handful of Republicans in Congress.

Meadows told reporters that the president was “very committed” to the deduction but did not identify it as a red line in the negotiations.

Republicans have also pushed back on the White House’s proposal to cut funding for COVID-19 testing and to tie school funding to reopening. But schools that do reopen fully will get more money because they will face additional challenges in providing transportation and meals while social distancing, Republicans said.

“We’re moving in the right direction I think on all fronts,” Sen. Roy Blunt (R-Mo.) said when asked about the testing money.

Many other areas of disagreement remain.

Senate Republicans are insisting on liability protections for businesses that reopen amid the pandemic, an idea Democrats don’t like because they would rather ensure workers are protected. House Democrats want funding for state and local governments, but Republicans have been opposed to what they call a “bailout” of states led by Democrats.

The White House and Republicans are hoping for a bill that costs about $1 trillion, while Democrats feel more funding is needed.