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House Speaker Nancy Pelosi told her caucus on a conference call Tuesday that she plans to keep members in Washington, D.C., until a deal is reached on a coronavirus relief proposal, a process that's been stalled for months since the House passed its initial $3 trillion-plus bill in May.

A source who was on the call said Democratic House members agree with Pelosi's plan to stay in town until a bill is passed.

The House is traditionally out of town for much of late September and October as members scatter to their districts for the stretch run of their reelection campaigns. If Pelosi keeps members in D.C. until a coronavirus relief package is passed it could harm vulnerable incumbents of both parties who could otherwise be meeting with constituents in their efforts to remain in office. But House Majority Leader Steny Hoyer, D-Md., noted the deal would be negotiated at the leadership level so rank-and-file members would not necessarily need to stay in their offices every day.

"I just got off a call with my colleagues. We are committed to staying here until we have an agreement, an agreement that meets the needs of the American people. We're optimistic that the White House at least will understand that we have to do some things," she said in a subsequent interview on CNBC.

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Rep. Hakeem Jeffries, D-N.Y., the House Democratic Caucus chairman, added Tuesday that Democrats "expect to be here as long as it takes in order to get something done on behalf of the American people" while listing off priorities including unemployment insurance, rental assistance, another round of stimulus checks and state and local government funding.

The move by Pelosi comes as Democrats and Republicans have had little luck finding common ground on a further coronavirus relief package.

Republicans earlier this summer came out with a $1 trillion proposal that struggled to gain traction within their own caucus before stalling. Then last week a smaller $300 billion bill proposed by Republicans was filibustered by Democrats who said the legislation was not nearly bold enough.

Senate Minority Leader Chuck Schumer, D-N.Y., and Pelosi have attempted to convince Republicans to meet them in the middle of the Democrats' more than $3 trillion proposal and the Republicans' opening $1 trillion offer -- at just over $2 trillion -- but the idea has been a nonstarter with Republicans, who have indicated they have little interest in passing another multitrillion spending bill after passing the $2.2 trillion CARES Act earlier this year.

"The cynical Republican COVID bill was emaciated, inadequate and designed to fail," Schumer said of the GOP bill his caucus filibustered last week. "Americans need help now, and Congress needs to respond in a way that meets the nation’s very real and urgent needs."

Senate Majority Leader Mitch McConnell, R-Ky., however, accused Pelosi and Democrats of pushing an unrealistic "wish list" that's standing in the way of doing at least something.

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"A few months ago, Speaker Pelosi wrote a massive, multitrillion-dollar liberal wish list that even her own House Democrat members said would never become law," McConnell said last week.

He added: "But in July, when Senate Republicans put forward a serious offer, Speaker Pelosi and the Democratic leader said they would not even talk unless we started with that unserious bill. No help for families unless they got to pass the absurd bill their own Democratic members had ridiculed. So in August, Republicans tried something else. We proposed breaking off some of the most urgent, most bipartisan policies and agreeing wherever we could ... But Speaker Pelosi and the Democratic leader blocked that too."

There may be some breaking in the Democratic coalition, however, as pressure ratchets up on both sides of the aisle to do something as the election nears and the pandemic continues.

The bipartisan House Problem Solvers Caucus released a $1.5 trillion coronavirus plan Tuesday, with one lawmaker telling Fox News its "goal is to get people back to the table."

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There was also a push on the House Democrats' call by Rep. Josh Gottheimer, D-N.J., and some others Tuesday for Democratic leadership to engage with the Problem Solvers Caucus' proposal. One Democrat on the call confirmed that those in close races "were really pressuring [Pelosi] to get something done."

But party leadership is resistant to changing its position even as individual members face pressure with the election coming up fast. Jeffries said Tuesday that Democrats are being fair by agreeing to come down from $3.4 trillion in the HEROES Act to $2.4 trillion while slamming Republicans and President Trump for allegedly showing "depraved indifference to human life."

"That is an incredibly reasonable public negotiating concession," Jeffries said. "But we have to have partners willing to do something meaningful."

Hoyer said that the Problem Solvers Caucus proposal is "lower than would be a responsible deal."

Fox News' Chad Pergram contributed to this report.