America could soon be swimming in COVID-19 vaccine. The shift from scarcity to surplus could bring its own problems.

In just two months, the United States may be swimming in COVID-19 vaccine. Literally swimming. The 500 million 0.5 or 0.3-milliliter doses expected to be shipped by then are enough to fill a 55,000-gallon swimming pool.

As hard as it is to imagine now as people frantically call, click and line up to get vaccinated, the nation is close to shifting from a situation of scarcity to one of abundance.

“It's not a switch that flips, but it's a sliding scale that happens differently community by community,” said Andy Slavitt,...