Both Ms. Pelosi and Mr. McConnell have scrapped plans for their chambers to reconvene next week, announcing that they would push the date until May 4 at the earliest, amid a raging debate over when it is safe for the country to begin pulling back on the social distancing practices that have slowed the spread of the coronavirus. And lawmakers in both parties say the strategy House leaders employed to pass coronavirus relief legislation in recent weeks — scheduling consensus action without a recorded vote and hoping that nobody will object — is not sustainable.

Deprived of the ability to meet in person, the House last month passed a $2 trillion stimulus package by voice vote — an unusual maneuver that almost fell apart when one lawmaker, Representative Thomas Massie, Republican of Kentucky, objected and demanded a quorum. Some members drove or flew all night to get to the Capitol to ensure the bill could pass.

Now, lawmakers are debating yet another emergency infusion of cash into the battered economy, and it has become painfully clear that the bipartisan cooperation that smoothed the way for the last bill to pass has evaporated, with Democrats and Republicans at odds over what should be included in a next round of government assistance.

Rank-and-file members in both parties and both chambers say it is too dangerous for them to return, and they want to avoid a repeat of the Massie episode. Moreover, they do not want legislation hashed out in private by their leaders. They want a chance, they say, to do what Congress is meant to do: debate legislation, offer amendments and vote.

“It’s time for Congress to come into the 21st century in terms of this issue,” said Senator Rob Portman, Republican of Ohio, who is sponsoring a bipartisan bill that would allow Senate leaders to authorize remote voting for 30 days in an emergency. “Probably half my constituents are working remotely right now, in full or in part, and Congress hasn’t yet figured it out. I think we’re a little behind the times.”