Under the Mnuchin plan, direct payments — on a means-tested basis — could be sent to American via the IRS as early as next month, although even that may not be as fast as some in Congress want.

"I think there is a high level of interest among our members in that idea and seems it might be an area where there's some common ground with Democrats as well," Thune told reporters following the Republican lunch.

Sen. Josh Hawley (R-Mo.), who has proposed a similar plan, said Mnuchin told senators the administration "could stand that up pretty quickly ... and get pretty significant relief out there pretty fast."

Senate Democrats have proposed their own $750 billion "Phase 3" plan to deal with the growing crisis, but President Donald Trump and Republicans seem ready to outbid them on government spending to help rescue the economy.

And while the idea of sending cash payments directly to Americans just might have been anathema to Republicans just a few weeks ago, ideological lines are being blurred quickly as the coronavirus crisis continues to spread, with more than 5,300 positive cases reported in the United States.

"These are not ordinary times. This is not an ordinary situation," McConnell said a press conference. "So it requires extraordinary measures."

The Senate will also take up and quickly pass a House-passed, $100 billion coronavirus stimulus bill referred to as "Phase 2." Senate GOP aides said the bill could be through the chamber as early as Wednesday. Senate GOP leadership took the pulse of members on the House bill Tuesday in order to speed up passage but there were objections, according to two sources familiar with the matter.

That Phase 2 package, hammered out in talks between Mnuchin and Speaker Nancy Pelosi (D-Calif.), provides paid sick days and emergency leave for employees who become infected or have to deal with family members who are sick.

McConnell said there had been some consideration of holding onto the Phase 2 bill until the Phase 3 proposal was ready and then merging them, but he decided against it.

The Kentucky Republican also noted that some of his rank-and-file members didn't like the House bill, but said, "My counsel to them is to gag and go for it anyway even if they think it has some shortcomings, and to address those shortcomings in the bill we're in the process of crafting."

McConnell said he'd created three Republican task forces to put together the Senate GOP version of a Phase 3 bill. Once that's done, McConnell said he would then enter into negotiations with Minority Leader Chuck Schumer (D-N.Y.) to come up with a bipartisan package that can win at least 60 votes.