Ms. Pelosi’s spokesman said she backed Mr. McGovern’s plan, which if approved by the House would pave the way for the first time in the history of Congress for members to cast votes other than in person. It would allow lawmakers who could not travel to Washington because of the pandemic to give specific instructions on each vote to a colleague authorized to vote on their behalf.

With Congress sidelined by the pandemic and unable to return to Washington until May at the earliest, Ms. Pelosi and Senator Mitch McConnell, Republican of Kentucky and the majority leader, have been under mounting pressure to come up with alternative ways of conducting business. Their current means of operating — trying to push through legislation on a consensus basis and hoping that nobody will object — is increasingly untenable, with partisan divisions mounting over what to include in the next round of coronavirus relief.

Other senior Democrats, including Representative Steny H. Hoyer of Maryland, the majority leader, have embraced the concept of remote voting in one form or another in recent days.

In an interview, Mr. McGovern described proxy voting as a “low tech” solution that struck a middle ground, enabling lawmakers to vote in person or not, depending on their preference and ability to return to Washington. Unlike electronic voting, he said, proxy voting could be instituted immediately without having to test new technology or worry about security breaches or interference by foreign actors.

“This is what we’re comfortable with doing now that I think poses the least amount of risk,” he said. “For those who feel they want to be here and engage in debate, they can come back, but for those members who are in states where they are instructed not to leave their homes or not to travel, they can still participate.”