WASHINGTON — With multiple lawmakers reporting potential exposure to the coronavirus on Monday, Congress faced difficult questions about whether to curtail its activities in the coming days, a step leaders are resisting even as fears rise.

Representative Julia Brownley, Democrat of California, said Monday that she was closing her offices in Washington for a week after meeting there with a person who later tested positive for the virus.

Her announcement came as three Republican representatives, Mark Meadows of North Carolina, Doug Collins of Georgia and Matt Gaetz of Florida — two of whom have spent time with President Trump in recent days — said they would self-quarantine after being informed that they had interacted at the Conservative Political Action Conference with someone who has tested positive. Senator Ted Cruz of Texas and Representative Paul Gosar of Arizona, both Republicans, took similar steps after earlier coming into contact with the same person.

The incidents underscored the balancing act congressional leaders confront in protecting themselves, their staffs and the thousands of people who move through the Capitol complex each day without unsettling a public that is accustomed to seeing its government working in times of crisis.