Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE (R-Ky.) on Tuesday said the Senate will not leave Washington until they pass a broader economic stimulus package as the coronavirus takes a growing toll on the markets.

How lawmakers pass a third stimulus package remains in flux, with one idea being floated to add “phase three” — expected to focus on small business and industries — into the House bill, which Senate Republicans say they view as a starting point.

“And it is my intention that the Senate will not adjourn until we have passed significant and bold new steps, above and beyond what the House passed, to help our strong nation and our strong underlying economy weather this storm," McConnell said from the Senate floor.

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He added that Senate Republicans viewed the House legislation as a "noncomprehensive bill" that can "only be the beginning of our efforts to support our health system, assist individual Americans and families, and stabilize the U.S. economy."

Republicans have been particularly critical over concerns that the House-passed bill does not do enough to help small businesses, even as restaurants, bars and other companies are restricting their activities or temporarily closing down altogether.

The House-passed bill covers up to two weeks of paid leave for the coronavirus, but exempts companies with more than 500 employees and would allow those with fewer than 50 to ask for a waiver.

“In particular, it seems increasingly clear that the House’s effort to mandate that small businesses provide new worker benefits, just as many small businesses themselves are in major jeopardy of their own, might even be actively harmful unless we urgently address a broader package that includes more and broader small business relief," McConnell added on Tuesday.

The administration is expected to pitch Senate Republicans on a third coronavirus package worth approximately $850 billion.

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The House has already passed a second coronavirus package, focused on paid leave and bolstering unemployment insurance. They are not expected to return to Washington until there is a deal on a third package.

The Senate could pass that bill as soon as Tuesday. But senators are under growing pressure to take additional action as growing concerns about a widespread coronavirus outbreak have cratered the economy.

Sen. John Thune John Randolph ThuneWhat Senate Republicans have said about election-year Supreme Court vacancies The Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump contradicts CDC director on vaccine, masks MORE (S.D.), the No. 2 Republican in the Senate, stressed that no final decision had been made on legislative strategy, underscoring the fluidity of negotiations between lawmakers and the White House.

“I think what we’re looking at is sort of the House-passed version as sort of the baseline and the building from that,” Thune told reporters.

“There’s definitely going to have to be a round three of this. ... How it gets across the floor and back to the House remains to be seen. It could move separately but maybe there’s a way it could be combined,” Thune added.

Thune hedged on making changes, noting they also didn't want to slow down coronavirus legislation.

"I think if we did add to the House passed package it would probably be things that everybody here would agree needed to be added," Thune said. "We're not going to slow the process down on the House-passed package unless there's a good reason to do it, and that would mean trying to make that package better and more responsive."