On Capitol Hill, the lawmakers charged with stanching the economic fallout signaled that a brokered stimulus deal might take longer than planned. The fate of a multibillion dollar emergency relief package that passed the House overwhelmingly early Saturday seemed uncertain as lawmakers and staff rushed to complete a package of technical changes to the legislation on Monday, even as more offices transitioned to working remotely and at least one lawmaker, Representative Ben Ray Luján, Democrat of New Mexico, announced he would self-quarantine.

Shortly after 8 p.m. Monday, the House approved the legislation with its technical changes, using a procedural maneuver that allowed — without the entire chamber present — for the legislation to head to the Senate. Earlier in the day, Representative Louie Gohmert, a Texas Republican with a knack for courting controversy, indicated that he might object to the effort on the grounds that the process was rushed, but ultimately agreed to allow the bill to pass.

It is unclear how quickly the legislation will move in the Senate.

Multiple Republican senators have voiced concerns with the package, particularly provisions that would establish paid sick leave and efforts to help businesses comply with that mandate. Senators and staff have discussed either amending or voting against the proposal, which was largely negotiated between Speaker Nancy Pelosi of California and Steven Mnuchin, the Treasury secretary.

Mr. Trump, who announced his approval for the measure on Twitter late Friday night, appeared to endorse possible Senate changes, telling reporters on Monday, “I think they may make it even better.”

And beyond that, lawmakers were floating ideas for another, even larger economic stimulus package that both parties agreed would most likely be necessary.

Senate Republicans have opened discussions on a follow-on bill to buffer the economy against the coronavirus. The bill could include direct aid like loans or grants for industries such as the airlines. The U.S. Chamber of Commerce called on Monday for Congress to approve loans and loan guarantees for large companies whose business has been disrupted by the virus.

Senator Mitch McConnell, Republican of Kentucky and the majority leader, said that any future legislation would help support families and bolster businesses and the health care system, indicating that he and his lieutenants would take a larger role in drafting another piece of legislation. Senator Chuck Schumer of New York, the Democratic leader, proposed allocating at least $750 billion to provide, among other things, immediate loan payment forbearance, affordable testing and emergency child care funding.