WASHINGTON — In another workplace, in another town, the news that a colleague who, days and even hours before testing positive for the novel coronavirus, had been dining and meeting and working out alongside his co-workers might have spurred some drastic measures.

Not so in Congress.

Senator Rand Paul’s announcement on Sunday that he had tested positive for the virus did little to alter the course of business on Monday in the Senate, where lawmakers continued to meet, spar and vote as leaders and top administration officials worked frantically to negotiate the largest economic stimulus measure in modern history.

As states, cities and employers around the country direct Americans to stay at home and shelter in place to slow the spread of the coronavirus pandemic, the Senate — nearly half of whose members are 65 and older — continues to defy the recommendations of public health experts. Mr. Paul’s diagnosis, which prompted two other Republican senators to quarantine themselves, only underscored the danger of the situation.

“It is naïve for us to believe that this is the end of the challenge to our membership,” said Senator Richard J. Durbin of Illinois, the second-ranking Democrat, imploring his colleagues to shutter the Senate and institute remote voting, an idea that has been resisted by congressional leaders in both parties. “We should not be physically present on this floor at this moment — we know better.”