The issue became more urgent late Wednesday, after Representatives Mario Diaz-Balart, Republican of Florida, and Ben McAdams, Democrat of Utah, disclosed that they had fallen ill after voting on the House floor early Saturday, and later tested positive for the virus. Between them, the two could have transmitted the virus to colleagues, many of whom are older. Congress’s attending physician was called in to trace their contacts.

“In. Person. Voting. Should. Be. Reconsidered,” Representative Debbie Mucarsel-Powell, Democrat of Florida, wrote on Twitter late Wednesday. “For the safety of our communities, during this emergency, we must be able to legislate from our districts.”

Congress has eschewed its usual voting rules before in times of national emergency, using unanimous consent, for instance, to enact urgent health relief measures to fight the Spanish influenza in the fall of 1918 when many members were either sick or scattered across the country. But the House and Senate have never allowed a member to cast a recorded vote from anywhere but inside their chambers, and any changes could be challenged on legal grounds.

It is that tradition that Ms. Pelosi and other senior lawmakers, many of them in their 70s and 80s, had in mind as they have forcefully shut down talk of voting from afar even as public health officials warned that their demographic was the most at risk.

Instead, they have suggested limiting the number of members on the floor, among other precautions.

Proponents of the changes argued they could be the best way to set an example for millions of constituents around the country who are being told not to travel or congregate in groups larger than 10, as well as to provide continuity at a time when more lawmakers are likely to grow sick or unable to travel.