Speaker Nancy Pelosi Nancy PelosiTrump puts Supreme Court fight at center of Ohio rally CDC causes new storm by pulling coronavirus guidance Overnight Health Care: CDC pulls revised guidance on coronavirus | Government watchdog finds supply shortages are harming US response | As virus pummels US, Europe sees its own spike MORE (D-Calif.) and House Democratic leaders are pulling out all the stops to get their restive and diverse caucus behind a sweeping $2 trillion coronavirus relief bill and send it to the president's desk as quickly as possible once they receive it from the Senate.

With the House on recess, lawmakers watched from afar as Senate leaders and White House officials hammered out the final bumps of the massive stimulus package in marathon negotiations over the past few days.

Pelosi was heavily involved in those talks, returning to Washington on Saturday, huddling with the bipartisan negotiators Sunday and keeping in constant communication with Senate Minority Leader Charles Schumer Chuck SchumerJacobin editor: Primarying Schumer would force him to fight Trump's SCOTUS nominee CNN's Toobin: Democrats are 'wimps' who won't 'have the guts' to add Supreme Court seats Republican senator says plans to confirm justice before election 'completely consistent with the precedent' MORE (D-N.Y.) as he ironed out the last wrinkles with Treasury Secretary Steven Mnuchin Steven Terner MnuchinShutdown clash looms after Democrats unveil spending bill Lawmakers fear voter backlash over failure to reach COVID-19 relief deal United Airlines, unions call for six-month extension of government aid MORE, leading to the announcement of a deal in the early hours of Wednesday morning.

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But House Democrats have felt cut out of the process, exasperated that, despite crafting their own $2.5 trillion emergency legislation, they've been denied the opportunity to exert more direct influence on the mammoth bill, the single largest stimulus package in the nation's history.

With that in mind, Pelosi and her team are racing to bring them on board, which is the only way the House can pass the measure quickly using procedural tools that would preclude the need for lawmakers to return to Washington amid growing fears of traveling and gathering in close quarters.

Democratic leaders have staged a series of conference calls this week, most recently on Wednesday afternoon, to tout the party's victories in the Senate bill. And Democratic committee heads have been conducting their own round of issue-specific calls on Wednesday to field concerns — and attempt to alleviate them.

As part of their pitch, they note that Congress is already working on a fourth round of emergency relief, where Democrats can fight to fill the voids they perceive in the third.

“This is a good bill. We’ll need a good fourth bill,” Rep. Brad Sherman Bradley (Brad) James ShermanSherman joins race for House Foreign Affairs gavel Castro launches bid for House Foreign Affairs gavel The Hill's Morning Report - Presented by Facebook - Trump, GOP senators at odds over next stimulus bill MORE (D-Calif.), a House Financial Services subcommittee chairman, told his Democratic colleagues on Wednesday’s leadership call, according to a source on the call.

On the other side of the aisle, House Minority Whip Steve Scalise Stephen (Steve) Joseph ScaliseHouse GOP slated to unveil agenda ahead of election House panel details 'serious' concerns around Florida, Georgia, Texas, Wisconsin elections Scalise hit with ethics complaint over doctored Barkan video MORE (R-La.) has urged his team and GOP committee leaders to support the Senate deal.

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“The American people are counting on us for quick, decisive action, and I’m confident we’ll come together at this time and rise to meet this challenge,” Scalise said in a statement.

The House is still waiting for the Senate to vote on the measure, which has hit a snag in the eleventh hour over unemployment provisions.

But Democratic leaders will soon face a daunting task. On one hand, they want to move the bill rapidly, wary that any delay will leave them open to attacks that they dithered while the economy tanked. On the other, they want to give their 232 members time to digest the enormous package — and record their gripes — as it just comes into view.

Complicating their efforts, the caucus is wildly diverse, with liberal lawmakers slamming the Senate bill as a corporate giveaway and moderate members urging quick passage to alleviate anxieties in their battlefield districts.

Rep. Stephanie Murphy Stephanie MurphyDemocrats scramble on COVID-19 relief amid division, Trump surprise Bank lobbying group launches ad backing Collins reelection bid House Democrats call on State Department for information on Uighur prisoner Ekpar Asat MORE (D-Fla.), co-chairwoman of the centrist Blue Dog Democrats, voiced those concerns on a caucus call Tuesday, warning that the House Democratic bill — chock-full of liberal provisions related to climate change, lobbying and labor law — had “set people off” by straying too far from the crisis at hand.

Amid the nascent debate, party leaders are leaving themselves some room to bring the package to the House floor.

On the call with rank-and-file members Wednesday, Pelosi made clear that, due to Senate delays, the House would not take up the package until Thursday at the earliest, according to a source on the call. And other leaders are broadcasting the same message publicly.

"Our goal is to get our caucus all of the information that they need and to get to unanimous consent or voice vote by tomorrow, certainly by Friday," Rep. Katherine Clark Katherine Marlea ClarkRep. Robin Kelly enters race for Democratic caucus vice chair Clark rolls out endorsements in assistant Speaker race Races heat up for House leadership posts MORE (D-Mass.), the vice chairwoman of the caucus, told MSNBC on Wednesday.

In a letter to Democrats Wednesday, House Majority Leader Steny Hoyer Steny Hamilton HoyerWhite House opposes House energy bill as Democrats promise climate action This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda House Democrats postpone vote on marijuana decriminalization bill MORE (D-Md.) vowed that leaders would provide lawmakers with at least 24 hours' notice before taking action.

How Democrats intend to vote on the package remains an open question. Pelosi on Wednesday signaled to her caucus that she prefers to pass the legislation quickly by unanimous consent, or UC; another option discussed was a voice vote.

House Minority Leader Kevin McCarthy Kevin Owen McCarthyMcCarthy's Democratic challenger to launch first TV ad highlighting Air Force service as single mother Trump asked Chamber of Commerce to reconsider Democratic endorsements: report The Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill MORE (R-Calif.) is pressing for the latter, warning Wednesday that some of his members want the opportunity to be on the floor voicing their objections.

"I don't think this can pass on unanimous consent," he said.

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Both UC and voice vote would require just a handful of lawmakers to be on the House floor, avoiding the need for all 430 members to fly back to Washington at a time when several of them have tested positive for COVID-19 or are showing symptoms.

A voice vote is preferred by some because it would allow critical lawmakers to shout their disapproval on the floor and then tell their constituents they voted against the stimulus. A number of conservative Republicans are urging that route.

But if a single lawmaker in the chamber — Democrat or Republican — objects to UC or requests a formal roll-call vote, Pelosi would be forced to call everyone back to Washington.

She and her team were scrambling Wednesday to find a way to allow lawmakers to record their votes on the enormous package without physically returning to D.C. But House Rules Committee Chairman Jim McGovern (D-Mass.) told his colleagues this week that so-called remote voting was not feasible, and Pelosi backed that message on Tuesday. Proxy voting, however, where a present lawmaker votes on someone else’s behalf, is still being looked at.

“The Speaker and majority leader (and minority leader) are searching for ways to get a legitimate, constitutional vote, without having to bring everyone back from across the country,” one House Democrat on Wednesday's leadership call wrote in an email. “But I have no idea what that will look like.”

One of the usual conservative rabble-rousers, Rep. Justin Amash Justin AmashOn The Trail: How Nancy Pelosi could improbably become president History is on Edward Snowden's side: Now it's time to give him a full pardon Trump says he's considering Snowden pardon MORE, an Independent from Michigan, said Wednesday he would not personally object if leaders tried to pass the bill by UC. But he said the House must find a way for lawmakers to record their vote on the largest stimulus package in American history.

“Otherwise, members of Congress have the opportunity to escape accountability for this legislation, which creates a moral hazard that leads to even less representative government and worse bills,” Amash tweeted. “We cannot let that happen.”

Updated at 5 p.m.