The House bill, called the American Health Care Act, had provisions that would have weakened current protections for people with pre-existing illnesses. It would have allowed states to eliminate Obamacare’s rules that health insurance must cover a standard set of benefits, like prescription drugs and mental health care, and its rule that insurance companies must charge the same prices to customers whether they are healthy or sick.

The House bill created a small pool of money for states to help sick customers who might be shut out of such markets. A majority of House Republicans voted for this bill.

Had this bill become law, the precise results would have depended on the choices by individual states. But the Congressional Budget Office estimated that nearly half of all Americans lived in a state that would have pursued such a waiver from standard benefits. The consequences, the C.B.O. said, would have been coverage that was unaffordable to many with pre-existing illnesses, along with holes in coverage for many serious conditions. For example, someone with a substance-abuse disorder might have lived where plans for people with that condition were very expensive and didn’t include addiction treatment.

The Senate considered several bills. A majority of Republican senators supported them all. Two would have included slightly different programs that would have allowed states to sidestep Obamacare protections.

Nearly every Republican incumbent who is now pledging to protect pre-existing conditions supported one of these measures. That’s true of Senator Ted Cruz of Texas, who once helped to shut down the entire federal government over a demand that Obamacare be reversed. It is also true of Dana Rohrabacher, a congressman from California, and Martha McSally, a congresswoman running for Senate in Arizona.

President Trump has said he continues to back repeal efforts. Mitch McConnell, the Senate majority leader, said recently that Congress would consider such legislation if Republicans retained their control after the election.

Several Republican senators have co-sponsored a bill that would ensure that people with pre-existing illnesses could buy insurance at standard prices if Obamacare were repealed or overturned. But that bill includes a large loophole: Insurers would not have to cover any care related to that condition. That bill is not scheduled for a vote, and the president has not endorsed it.