The number of tests that will actually be administered in the coming days could be substantially lower than the administration’s projection of one million by next week. A spokesman for the Department of Health and Human Services said on Monday that public health labs can currently test 15,000 people, and could test up to 75,000 by the end of this week.

The Association of Public Health Laboratories, which represents state and local government laboratories around the country, has said that its labs would be able to conduct about 10,000 tests a day when all of its 100 members that can perform testing are running. Scott Becker, the executive director of the lab association, said on Monday that labs can run about 100 tests per day. As of Monday, he said fewer than half of those labs were able to do so.

“All that matters is how many people you can test a day,” said Scott Gottlieb, who was the F.D.A. commissioner from 2017 to 2019.

As they learned on Tuesday that the death toll in their state had reached nine, the two Democratic senators from Washington pressed Mr. Pence and the health officials about both the administration’s response and its message to the public, particularly about the availability of testing.

“Our message to them was, be clear that they aren’t readily available, and the universe of people who have access to them is not large enough,” Senator Maria Cantwell said. “Let’s figure out a more aggressive plan.”

The state’s other senator, Patty Murray, said she had been hearing from constituents who were desperately calling “every number they can find” for information, and cannot get through.

“I think there’s a lot of concern about honest, accurate reflection of what is real when you have something like this happening,” Ms. Murray said.