Most Americans will be able to get their coronavirus vaccines between the middle of May and early June, President Biden's chief medical adviser Anthony Fauci told CNN on Tuesday.

Why it matters: That timeframe is slightly delayed from Fauci's previous projection of late March to early April, and it comes after Johnson & Johnson failed to meet its promised supply timetable due to lags in production.

What he’s saying: "It may take until June, July and August to finally get everybody vaccinated," Fauci said. "So when you hear about how long it’s going to take to get the overwhelming proportion of the population vaccinated, I don’t think anybody disagrees that that’s going to be well to the end of the summer and we get into the early fall."

• The U.S. government is expecting "considerably more" doses from J&J, which recently applied for emergency authorization, Fauci noted.
• The U.S. has purchased 100 million vaccine doses from J&J.
• But demand is still outpacing supply, which Fauci called "a critical issue."
• "I’m a little disappointed that the number of doses that we’re going to get early on from J&J are relatively small, but as we get further into the spring, there will be more and more."

Fauci doubled down on his warning that mutations pose a "clear and present danger" in a separate interview with "L.A. Times Today" on Tuesday.

• "Since this is a global pandemic, it will require a global response," Fauci said, referring to the U.S.'s participation in the global inoculation effort. "So we have to pay attention to what’s going on in the rest of the world.
• "Otherwise, we will be constantly threatened by variants and different lineages of the virus that will have evolved outside of the United States."
• "You will be seeing us playing our role in the global response, particularly in the arena of vaccinations," he added.

The big picture: In the U.S., vaccine distribution is so far restricted to essential workers, people ages 65 and older, and those with underlying health conditions, depending on the state.

• State health officials have repeatedly called on the federal government to provide a more robust supply of vaccines.
• Some mass vaccination sites have had to delay operations due to a shortage in vaccines, per CNBC.
• The U.S. has allocated $4 billion to COVAX, the global effort to ensure equitable access to vaccines.

Go deeper: Why vaccine production is taking so long

Editor's note: This story has been updated with Fauci's comments on "L.A. Times Today."