Ron Klain, who Mr. Biden tapped as his White House chief of staff, said Sunday that fewer than 1-in-3 Americans got a coronavirus test on the Trump administration’s watch, which he said was a forecast of problems to come with the distribution of vaccines.

“Now the question is how can we get 100% of Americans a vaccine in short order and that is a challenge that I think the American people are right to be skeptical about in terms of the way in which the Trump administration would handle it and that’s a challenge that is largely going to fall on the Biden administration,” Mr. Klain said on ABC’s “This Week” program. “The sooner we can get briefed on those plans, the sooner we can get our experts in with their experts, I think the more confidence everyone can have that those plans will proceed apace in 2021.”