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Mr. Obama has taken similar tactics with existing immigration law — directing his administration not to deport certain young people who agree to go to school or join the military — and with the Defense of Marriage Act, by refusing to defend it in court.

Some, such as federal Judge Brett M. Kavanaugh, have gone so far as to suggest that Mr. Romney could refuse to implement the health care law entirely, imitating Thomas Jefferson when he declined to enforce the Sedition Act on the grounds that it was unconstitutional.

But analysts say a move like that would be unlikely, given that the Supreme Court already has ruled that nearly all of the health care law is constitutional. By contrast, Mr. Obama’s refusal to argue for DOMA is a different matter because the court hasn’t yet ruled on that law, Mr. Hills said.

“The controversy is that [DOMA’s] not that obvious. The court hasn’t said it’s unconstitutional,” Mr. Hills said. “So it’s what we call an open question.”

Whatever tactics Mr. Romney chooses if he wins on Nov. 6, it’s expected he’ll do something to undermine the health care law, which he and Republicans have vowed to get rid of throughout the campaign season. Just minutes after the Supreme Court upheld the law in June, he stood in front of the Capitol building and promised to repeal the law on “Day One” of his presidency.