One of the Senate GOP’s leading voices on health policy on Tuesday warned that members of Congress could form a “virus spreading machine” when they return home.

Health, Education, Labor and Pensions Chairman Lamar Alexander expressed hope that the congressional leaders’ views would evolve and the attending physician would accept rapid coronavirus testing capability for lawmakers to check them before they depart Washington, D.C.

“From a public health point of view, this is not mostly about protecting members of Congress. It is about protecting the people members might infect,” the Tennessee Republican said in a statement issued after a Republican Conference lunch. “Bringing 100 or 535 members from across the country to Washington, D.C. — a coronavirus hotspot — and then sending them home each weekend creates a highly efficient virus spreading machine.”

Alexander made similar comments to reporters on Capitol Hill Tuesday, confirming he had discussed the matter with Senate Majority Leader Mitch McConnell, R-Ky.

McConnell and Speaker Nancy Pelosi of California announced in a rare joint statement over the weekend that they were turning down a Trump administration offer for rapid testing capability. Under White House policy, people in close contact with President Donald Trump and Vice President Mike Pence are tested for the coronavirus on a regular basis.

“Congress is grateful for the Administration’s generous offer to deploy rapid COVID-19 testing capabilities to Capitol Hill, but we respectfully decline the offer at this time,” McConnell and Pelosi had said. “Our country’s testing capacities are continuing to scale up nationwide and Congress wants to keep directing resources to the front-line facilities where they can do the most good the most quickly.”

As of May 4, Washington had a total of 5,170 confirmed cases and 258 deaths.

Alexander, generally a close ally of the majority leader, conceded some lawmakers may be concerned about the appearance that Congress would be putting itself ahead in the testing line if the institution accepted the rapid testing equipment. Alexander said that shouldn’t be an issue, “if you’re giving two million tests a week.”

“He knows my thoughts about that,” Alexander said of McConnell. “What I’ve said to him is that I think those attitudes are going to change very quickly.”

Alexander said that in the event senators or House members test positive after leaving the nation’s capital, it could “take an army of public health workers to track and trace all the people they might have exposed.”

“I think it would be better if we would check members of Congress before they go home,” he said. “The difficulty is exposing people on an airplane or exposing people in your home area.”