But in creating clear benchmarks for himself, Mr. Biden is taking a risk. He will undoubtedly be held to the 100 million promise at the 100-day mark on April 30, and fulfilling it will require no hiccups in manufacturing or distributing the vaccine and a willingness by Americans to be vaccinated.

Mr. Biden’s announcement came as fresh details emerged about how Pfizer, the pharmaceutical giant whose vaccine could receive regulatory approval in the United States this weekend, repeatedly urged the Trump administration to lock in a bigger supply. Before the vaccine was proved highly successful in clinical trials, the administration repeatedly turned down the chance to expand its pre-order beyond the 100 million doses it agreed to buy from Pfizer last July.

The administration is now seeking to double the pre-order; otherwise it will run out of Pfizer’s vaccine by around March, according to people familiar with the talks. But Pfizer may not be able deliver more doses for Americans until as late as June because the company signed deals with other governments, including the European Union, as the Trump administration hesitated.