The measure is not expected to be taken up in the Republican-controlled Senate, but House Speaker Nancy Pelosi signaled Thursday that she is open to negotiating.
One Republican -- Rep. Peter King of New York -- supported the bill because of the relief the measure would provide to state and local governments.
Fourteen Democrats voted down the bill, many of them claiming the measure didn’t go far enough to provide relief to millions of Americans who are economically struggling due to the public health crisis.
"We’re putting our offer on the table, we’re open to negotiation," Pelosi said Thursday, acknowledging the long odds of the bill becoming law.
In a letter sent to House members Thursday, Pelosi maintained that Republicans had previously supported many priorities that were included in this latest legislation.
"It is important to note that more than 80 percent of the priorities in the Heroes Act have been supported by the Republicans in the four previous COVID-19 acts of Congress. We are proud of how we built on that bipartisanship and look forward to negotiations For The People," Pelosi wrote.
The proposed legislation includes a second round of direct cash payments to Americans, $1 trillion in aid for local, state and tribal governments drowning under the strain of the novel coronavirus, assistance for essential front-line workers, an extension of unemployment benefits and various other Democratic measures.
The proposal, if it clears both chambers, would become the largest, most expensive spending package in U.S. history -- surpassing the $2.2 trillion measure Congress passed in March.
"This will not pass. It's not going to be supported," Sen. John Barrasso, a member of Republican leadership, warned earlier this week.
GOP Sen. Lindsey Graham told reporters the bill is "dead on arrival" in the Senate and pointed to the price tag, saying there are too many unrelated provisions included in the bill.
"I see that the House is going to move on a measure maybe as soon as Friday," Sen. Lisa Murkowski, a Republican from Alaska, told reporters Wednesday. "Without even looking at it, I really question whether that approach is really the way to go right now. We have put a lot out there, and we need to make sure it is getting to where it needs to go."
The coronavirus legislation is largely viewed as a "messaging bill" for Democrats and an opening bid in negotiations with Senate Republicans, who have blasted the bill as a "liberal wishlist."
"This week, the Speaker published an 1,800-page seasonal catalog of left-wing oddities and called it a coronavirus relief bill," Senate Majority Leader Mitch McConnell said on the Senate floor Thursday.
"Here we go again," he added, before slamming House Democrats for not reconvening as a chamber in recent weeks.
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The Capitol attending physician advised House leaders last week not to return to Washington as coronavirus cases are still on the rise in the nation's capital.
"House Democrats have been missing in action for months. While the Senate was passing the CARES Act, the Democratic House was on the sidelines — substantively, and literally. They had already gone home. Nearly two months later, senators are back at our duty stations, with new precautions. We've been back two weeks. We're holding major hearings on the pandemic, legislating, and confirming nominees. But the House is still at home. And when they do contribute, it's not serious," McConnell said.
"DOA. Dead on arrival. Of course, Nancy Pelosi knows that," Trump told reporters Wednesday at the White House.
Senate Minority Leader Chuck Schumer endorsed the House Democrats' bill and said he is "hopeful" Congress will strike a deal.
"Despite my worry and concern that our Republicans are sitting on the sidelines, I am optimistic we can get something done," the New York Democrat said Thursday during an interview with CNBC.
Schumer also slammed McConnell for wanting to wait and see how the previous stimulus packages Congress has passed will effect the economy before working on another bill.
"What alternative universe is he in?" Schumer said.
In their proposal, House Democrats have also pushed for expanded ballot access ahead of the November election in the case that the public health crisis makes in-person voting dangerous.
Trump on Wednesday bemoaned that the legislation was a "voting package" that would expand access to mail-in ballots, and he complained that it would disadvantage Republicans in future elections if passed into law.
"They want to be able to make sure that Republicans can't win an election by putting in all sorts of mail-in ballots," Trump said.
The House is also expected to vote on a remote-voting resolution Friday, which does not appear to have Republican backing.
This report was featured in the Monday, May 18, 2020, episode of “Start Here,” ABC News’ daily news podcast.
"Start Here" offers a straightforward look at the day's top stories in 20 minutes. Listen for free every weekday on Apple Podcasts, Google Podcasts, Spotify, the ABC News app or wherever you get your podcasts.