The House overwhelmingly approved legislation on Thursday that would relax the terms of a federal loan program intended to help small businesses weather the pandemic, giving companies more time and flexibility to use the money.

The measure would alter the Paycheck Protection Program to allow small businesses 24 weeks instead of eight weeks to spend the loan funds. Without congressional action, some loan recipients will hit the end of their eight-week period within days.

But the bill’s fate is uncertain in the Senate, where a bipartisan group of senators unveiled their own set of revisions last week, including a shorter, 16-week window for spending the loan money.

The bill’s near-unanimous passage in the House marked a rare bit of bipartisanship amid a bitterly partisan debate over the next round of federal coronavirus relief, with Democrats pressing for quick action to provide trillions more in spending and Republicans wanting to wait and consider a far leaner package.

House Democrats’ decision to expedite the changes to the loan program reflected a building sense of urgency among some moderates to put aside that broader dispute and find areas of agreement with Republicans where possible.

This month, House Democrats pushed through a $3 trillion pandemic relief package over Republican opposition, but that bill is doomed in the Senate and faces a veto threat from President Trump. The small-business measure, however, enjoyed strong enough bipartisan support that it was considered on Thursday under faster procedures reserved for noncontroversial bills, passing 417 to 1. Representative Thomas Massie, Republican of Kentucky, was the lone “no” vote.

“There’s been a lot of negotiations to find something that will make it through the Senate and hopefully be signed into law by the White House,” said Representative Dean Phillips, Democrat of Minnesota, who wrote the legislation along with Representative Chip Roy, Republican of Texas.

Mr. Phillips, one of several moderate Democrats who had been reluctant to support the $3 trillion bill given its dim prospects of becoming law, agreed to vote for it after extracting a promise from Speaker Nancy Pelosi to allow a vote on the narrower — and far more bipartisan — legislation to modify the Paycheck Protection Program.

“We intentionally wanted a skinny bill that addressed a very specific issue,” he added. “We listened, and we modified it and came to a nice bipartisan conclusion.”

The House rejected a separate bill put forward by Mr. Phillips that would toughen transparency requirements for the program, requiring that the administration release details about the recipients and the lenders, after Republicans opposed it.

Since its inception, the Paycheck Protection Program has been plagued by problems and controversy, but it has proved exceedingly popular with businesses, who have flooded the government with requests for the assistance, and has drawn bipartisan support. The initiative was created by the $2.2 trillion stimulus package enacted in March, and Congress moved last month to inject an additional $320 billion into the program as it ran out of money amid a glut of applications.

But the House legislation would also eliminate a number of restrictions, including limitations on how the loan money could be spent, in order to make the program more accessible to local restaurants, hotels and hospitality businesses. The legislation would lower the percentage of money required to be spent on payroll in order to have the loan forgiven to 60 percent from 75 percent, allowing loan recipients to spend more funds on utilities, rent and other business expenses.

In the Senate, the four architects of the original program — Senators Marco Rubio of Florida and Susan Collins of Maine, both Republicans, and Senators Benjamin L. Cardin of Maryland and Jeanne Shaheen of New Hampshire, both Democrats — have introduced their own modifications.

In addition to 16-week time frame for repaying the loans, it would allow recipients to use the funds — which were intended to primarily cover payroll expenses — to buy personal protective equipment for their employees, as well as renovations to accommodate additional safety measures, like installing a drive-through window, adding physical barriers or upgrading ventilation systems. Those changes were not included in the House legislation.

Mr. Rubio said in a statement that he had concerns with elements of the House legislation, arguing that “inadvertent technical errors” in it could discourage businesses from hiring back all of their workers.

Mr. Roy said the issues should not stand in the way of quick enactment of the changes.

“Let’s actually get this done,” Mr. Roy said in an interview. “There’s obviously a few concerns that people raise here and there — I find them to be much more theoretical than practical.”

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Senator Chuck Schumer of New York, the Democratic leader, supports the House legislation and plans to push for its consideration when the Senate returns Monday, a spokesman said.

Even if the two chambers were able to resolve their substantive differences, the bill faces an uncertain path in light of a Republican lawsuit filed this week that argued that any legislation passed with proxy votes is constitutionally invalid. The House voted on the small-business bill using new procedures pushed through by Democrats this month that allow any lawmaker to designate a member to act as his or her proxy on the House floor to record their vote during a pandemic-related emergency.

Senator Mitch McConnell, Republican of Kentucky and the majority leader, has signaled that his chamber might not take up any legislation passed out of the House under its new system.

But Mr. Roy, who joined the lawsuit challenging the legality of the new voting rules, said he doubted there would be any questions about his measure because it passed by such a wide margin.

“It certainly casts a cloud over any legislation that depended on the proxy votes to pass,” Mr. Roy said. “I believe that if the bill has passed with a legitimate number of in-person votes, and you had an in-person quorum, it’s a legitimate measure.”