Senate Majority Leader Mitch McConnell said Tuesday the Senate will stay in session until it passes "major legislation" to address the coronavirus crisis beyond the House's bipartisan proposal.

“We are crafting the major legislation that the American people deserve in the face of this major challenge," McConnell, R-Ky., said from the Senate floor Tuesday morning.

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“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's comments come as the nation's economy is grinding to a standstill with travel curbed, schools shuttered, workers at home, professional sports sidelined and restaurants in major cities closing their dining rooms. Beyond sickness and death, the coronavirus response has already caused hardship to Americans' bank accounts and businesses' budgets. And pain is expected to continue for some time, with the White House projecting the outbreak to continue through the summertime.

“This is a moment for bold and bipartisan action," McConnell said.

The Senate Tuesday is taking up the bipartisan legislation the House passed early Saturday with broad support, including the blessing of President Trump. The legislation would make coronavirus testing free, offer 14 days paid sick leave to workers, set up emergency family leave and expand unemployment benefits and food assistance.

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But McConnell downplayed the House legislation -- likely to pass the Senate -- as a non-comprehensive bill that can only be the beginning of the congressional response. He warned that the new coronavirus worker benefits for paid absences may actually be "actively harmful unless we urgently address a broader package that includes more and broader small business relief."

GOP senators were to lunch with Treasury Secretary Steve Mnuchin Tuesday on Capitol Hill to discuss another round of legislation. McConnell said the package should include more direct financial assistance for American workers and families, support for small businesses and resources for the medical sector to fight the new virus on the front lines.

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Fox News has learned that the White House specifically is pushing an $850 billion stimulus, largely in the form of tax relief measures. But Mnuchin told reporters at a Tuesday briefing that they also are looking at sending Americans checks "immediately."

Meanwhile, Senate Democratic Leader Chuck Schumer, D-N.Y., is to hold a conference call with Democrats in place of the regular weekly lunch to unveil his own $750 billion proposal.

Schumer urged the Senate to pass the House bill today to send to Trump and then move on immediately to a big economic stimulus package.

"Our major focus cannot be based on bailing out airlines, cruises, and other industries," Schumer said. "We must first prioritize economic solutions that are focused on workers and their families."

Fox News' Tyler Olson and John Roberts contributed to this report.