The recent court rebukes have only increased the focus on the Supreme Court and the impact that Justice Anthony M. Kennedy’s retirement could have. Beyond abortion rights, which are sure to be a focus of Senate confirmation hearings, other health care issues could be in the balance.

The court upheld the Affordable Care Act in 2012, but challenges to various provisions are still pending in lower courts. In addition, the Supreme Court is being asked to decide questions with major implications for the future of Medicaid: whether states can exclude Planned Parenthood clinics from their Medicaid programs, and whether Medicaid patients can sue states to enforce their rights under federal law.

“Any presidential administration is going to try and push as hard as it can to use its executive powers to the limit,” said Sara Rosenbaum, a professor of health law and policy at George Washington University. “But this administration is reframing the purpose of health care laws to pursue its own preferred agenda. That’s what the courts have found.”

The administration’s troubles in courts are somewhat surprising since Alex M. Azar II, the secretary of health and human services, emphasized the importance of following proper procedures when he served in the George W. Bush administration as general counsel at the department.

“Clients always want to do things quickly, especially when you are dealing with the public health and welfare,” Mr. Azar said in a 2004 speech. “But we try to convince our clients that it will serve their interests by doing things the right way. Often, this means using notice-and-comment rule-making, which can be a long and arduous process.”