WASHINGTON — Obama administration officials knew they were on shaky ground in spending billions of dollars on health insurance subsidies without clear authority. But they did not think a long-shot court challenge by House Republicans was cause for deep concern.

For one thing, they would be out of office by the time a final ruling in the case, filed in 2014, was handed down. They also believed that a preliminary finding against the administration would ultimately be tossed out. Finally, they figured that President Hillary Clinton could take care of the problem, if necessary.

Well, they are out of office, Mrs. Clinton is not president and the uncertain status of the cost-sharing payments now looms as the biggest threat to the stability of the insurance exchanges created under the Affordable Care Act. A dubious decision made by the previous White House has handed the current administration a powerful weapon to wield against the health care legislation that it despises.

“The administration should not have found an appropriation where none existed,” said Nicholas Bagley, a University of Michigan law professor who has studied and written about the issue. “The Obama administration argument that the Affordable Care Act included an appropriation for the cost-sharing payments never held water.”