Senate Majority Leader Mitch McConnell revealed Tuesday morning that Senate Republicans plan to support another round of stimulus checks - or “direct payments” - to Americans in their next coronavirus relief proposal.

In a Senate floor speech, McConnell gave no details on just who Republicans think should get this next round of checks.

Most Republicans wants a lower income threshold to qualify. The cap on payments in the first CARES bill was $99,000.

McConnell made the announcement as top White House officials were set to come to Capitol Hill to tell Senate Republicans what President Donald Trump wants in the relief package -- including a payroll tax cut -- and cuts in proposed funding for testing an the Centers for Disease Control and Prevention -- items many Senate Republicans oppose.

Later Tuesday, Treasury Secretary Steven Mnuchin and White House Chief of Staff Mark Meadows were to meet with House Speaker Nancy Pelosi. House Democrats are pushing for much more than the $1 trillion package McConnell wants -- including considerably more in extra unemployment benefits due to stop at the end of the month.

McConnell outlined other key components of the Senate Republican proposal for the next phase of COVID-19 legislation, the clearest outline of the Republican plan so far presented.

Besides advocating a second round of direct payments to Americans, he also said that he'll push for a second round of the Paycheck Protection Program "with a special eye for hard-hit industries."

The Republican proposal also includes, McConnell said, $105 billion for schools plus additional money for child care and reimbursements for safe workplace initiatives -- including funding for remodeling, cleaning and personal protective equipment. The package would also include funding aimed at speeding vaccine production and provide liability protections for businesses, schools and health care providers.

Provisions to get workers back to work are also being looked at with "laser focus," McConnell said, though he did not outline the specifics of those policies.

"The United States of America was not built for a defensive crouch," McConnell said. "We need to stand up an educational system and an economy that works for workers and families at the same time. We need to find the right sort of middle ground."

It's not yet clear how Democrats will respond to the proposal, though they've been critical of a drafting process that did not include their input.

Speaking on the Senate floor just after McConnell, Minority Leader Chuck Schumer said that based on what he's seen in news reports the Republican proposal "appears destined to fall drastically short of what is required."