WASHINGTON — The Supreme Court agreed on Monday to hear a third major challenge to the Affordable Care Act, setting up likely arguments this fall in a case that could wipe out President Barack Obama’s signature domestic achievement.

The court granted requests from Democratic state officials and House members who wanted to thrust the fate of the Affordable Care Act into the public eye just as Americans prepare to vote this November. The Supreme 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 focus political attention on the health law’s most popular provisions — like guaranteed coverage for pre-existing medical conditions, emergency care, prescription drugs and maternity care — and to ensure that the case was decided while justices who had rejected earlier challenges to the law remain on the court.

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

The case the justices will hear was brought by Republican state officials, who argued that when Congress in 2017 zeroed out the penalty for failing to obtain health insurance, lawmakers rendered the entire law unconstitutional. The Trump administration sided with the state officials, arguing that the rest of the health care law could not survive without a penalty for flouting the requirement that most Americans have health insurance, sometimes called the individual mandate.