The division between the national Republican leadership and Mr. Romney lasted just a few days. His advisers described the situation as untenable, and decided that the semantics game was not worth playing. It was confusing voters, they said, and it was distracting the campaign from its broader message that Mr. Romney would repeal Mr. Obama’s health care plan.

As Mr. Romney prepared to march in the Fourth of July parade in Wolfeboro, N.H., where he owns a vacation home, on Wednesday, his aides anticipated that reporters would shout questions at him on the issue. They decided to have Mr. Romney describe the president’s mandate as a tax in an interview with CBS News.

“The Supreme Court has the final word, and their final word is that ‘Obamacare’ is a tax, so it’s a tax,” Mr. Romney said in the interview, though he asserted that the court’s opinion also supported the contention that his own mandate in Massachusetts was merely a “penalty.”

The distinction is technically accurate. Without directly referring to Massachusetts, Chief Justice John G. Roberts Jr. wrote in the court’s majority opinion that a governor could design a health care mandate under the authority that all states enjoy to carry out laws without resorting to a specific taxing authority. Broader “police powers,” Chief Justice Roberts wrote, are reserved to the states, which “do not need constitutional authorization to act.”

But whatever the legal justification, the law signed by Mr. Romney used the tax system to enforce the mandate, seizing on an idea that had become popular among conservative scholars at the time. In his later book, “No Apology,” Mr. Romney said taxes would provide the necessary incentive to persuade people to purchase health insurance.

Creating the right incentives, he wrote, “can be done by reducing tax deductions for people who don’t buy insurance — as we did in Massachusetts — or by giving tax credits to all those who do.”

After quoting a Harvard professor about the “tax penalty” in the Massachusetts plan, Mr. Romney wrote that “the results have been remarkable,” adding that “despite the requirement that individuals buy insurance and that employers either provide coverage or pay a tax, the program has remained extremely popular.”