In California, where thousands are being monitored for the virus, only 516 tests had been conducted by the state as of Thursday. Washington health officials have more cases than they can currently process. And in New York, where cases have quadrupled this week, a New York City official pleaded for more test kits from the Centers for Disease Control and Prevention…

In the last week, Mr. Trump and his top officials repeatedly promised that 1 million to 1.5 million tests would be sent around the country, even though labs — government and private ones alike — have struggled to get the tests running amid a growing number of infections and rising demand for tests. Despite an order Wednesday by the C.D.C. to greatly expand criteria for who can be tested, many hospitals and state health authorities continued to limit tests to those at the highest risk for infection, adding to the confusion and frustration, especially in hot spots like California and Washington…

Over the past few days, Vice President Mike Pence has been moderating expectations about how quickly the tests would be widely available. On Friday, Mr. Pence said it would be a “matter of weeks” before Americans could get easy access to a coronavirus test.

And on Thursday, he seemed to acknowledge that the administration’s estimates were high.