The court did not say when it would hear the case, but, under its ordinary practices, arguments would be held in the fall and a decision would land in the spring or summer of 2021.

Democrats, who consider health care a winning issue and worry about possible changes in the composition of the Supreme Court, had urged the justices to act quickly even though lower courts had not issued definitive rulings. They wanted to keep the fate of the Affordable Care Act, sometimes called Obamacare, in the public eye during the presidential campaign and to ensure that the appeal was decided while justices who had rejected earlier challenges remain the court.

In the meantime, the law remains almost entirely intact but faces an uncertain future.