The legislation, which grants more funding to state and local governments, coronavirus testing and a new round of direct payments to Americans, sets up an immediate clash with the Republican-controlled Senate, where leaders have said another round of emergency funding is not yet need for.
Democrats released the 1,815-page legal text on the bill Tuesday afternoon, and House Speaker Nancy Pelosi spoke from the US capital after its introduction.
Pelosi was aiming for Republican congressmen who have argued that it would be better to first evaluate how already adopted aid is being implemented before moving on to a new relief law.
"For the families who are suffering, hunger does not take a break, rent does not take a break, bills do not take a break, difficulties in losing a job or tragically losing a loved one do not take a break," Pelosi said, describing the crisis as "a historic challenge" and "a significant opportunity for us to meet the needs of the American people, to save lives, livelihoods and democracy."
But Republican leaders in the Senate warned Pelosi that the new bill had died on arrival even before it was formally unveiled.
"It will not pass. It will not be supported," said Senator John Barrasso, a member of the Republican leadership in the chamber.
House Majority Leader Steny Hoyer, a Maryland Democrat, said in a notice to members Tuesday afternoon that the House is expected to meet Friday morning to vote on the legislation.
The package is expected to cost more than $ 300 trillion, according to a senior House Democratic aide. Three other aides also told CNN that the price tag would be in the $ 3 trillion series. It would dwarf the stimulus survey that was launched in March, which was more than $ 2 trillion and at that time constituted the largest emergency relief package in American history.
House Democrats have pushed ahead with a new stimulus package amid fierce opposition from Republican lawmakers and the White House, who say they will wait to see the impact of previously adopted relief measures before moving on with a new package.
Without any Republican support, the bill cannot be passed in the Senate. But the unveiling of legislation now gives Democrats the opportunity to showcase their priorities and outline their legislative vision of how to help a country in serious strains as a result of the devastating pandemic.
Republican Senator John Cornyn reiterated Tuesday that he believes there is no "urgency" to enact another coronavirus relief law when asked if the Senate is likely to wait until after Memorial Day's recess to introduce phase four legislation.
"I don't think there's a sense of urgency to do it now, because a lot of the money we've already appropriated hasn't even gone out the door yet," the Texas Republican told reporters. "So we take one day at a time."
Republican Senator Lindsey Graham said the bill is "dead on arrival" in the Senate.
In phase four, Graham also said "Oh, God, no, no way" about whether the Senate will pass a new coronavirus bill before Memorial Day. But he added that he is "sympathetic" to the idea that the economy will need extra help to recover.
But there are a number of potentially important sticking points to any bipartisan agreement on a new round of emergency funding.
Senate Republicans have argued that accountability reforms to protect employers from the rash of lawsuits must be included in all upcoming legislation, a requirement Democrats have met.
"Our focus has been to protect people, not protect people from harming them and have no responsibility for harming them," he said.
Democratic leaders are also planning to move forward with a work plan for external voting and external committee Friday, Hoyer said.
He said he is disappointed Democrats and Republicans have failed to reach a consensus vote, although party leaders continue to work for a deal.
"I hope we get there, but we definitely need to get there and we need to get there quickly," he said. He reiterated that if there is no agreement, the Democrats will continue with their own plan.
This story has been updated to include additional information and reaction.
CNN's Ali Zaslav, Lauren Fox and Ted Barrett contributed to this report.