President Joe Biden will meet his goal of vaccinating 100 million Americans in his first 100 days in office early, according to Dr. Scott Gottlieb.

"We'll get 100 million Americans vaccinated probably by early April," Gottlieb, who was FDA chief during the Trump administration, predicted. Biden's 100th day in office is April 30.

While there is currently not enough supply of Covid vaccines to meet demand, the nation will soon have the exact opposite problem. Earlier Wednesday, Biden announced plans to buy another 100 million doses of Johnson & Johnson's single-shot vaccine. Added to the doses from Pfizer and Moderna, it is more than enough supply to vaccinate every American.

Gottlieb said that he thinks "the bigger issue" will be when demand drops off. In order to stimulate demand in the U.S., he told CNBC's "The News with Shepard Smith," officials must make the vaccine "more accessible," and that includes running clinics where people don't have to sign-up for a vaccine ahead of time.

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