Opponents of President Barack Obama’s signature legislative achievement have made what may be a self-fulfilling prophecy: They repeatedly forecast the collapse of the health law, and then push it along.

Frustrated state officials have ideas for stabilizing the individual insurance market, but they say they cannot figure out where to make their case because they have been bounced from one agency to another in the Trump administration.

“We have trouble discerning who has decision-making authority,” said Julie Mix McPeak, the Tennessee insurance commissioner and president-elect of the National Association of Insurance Commissioners, which represents state officials. “We reached out to the Department of Health and Human Services. They referred us to the Office of Management and Budget, which referred us to the Department of Justice. We reached out to the White House Office of Intergovernmental Affairs.”

The Trump administration has sent mixed signals, reflecting an internal debate about whether to stabilize insurance markets or let them deteriorate further. Mr. Trump has said he could cut off the subsidies at any time if he wanted to.

The government may clarify its plans in a legal brief to be filed on Monday with the United States Court of Appeals for the District of Columbia Circuit. Or it could simply ask the court for a three-month extension, prolonging the uncertainty.