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The health care law requires most Americans to obtain health coverage, and imposed an IRS penalty on those who fail to do so. During the debate, Mr. Obama said that wasn’t a tax: “For us to say ‘You have to take responsibility to get health insurance’ is absolutely not a tax increase.”

By the time the lawsuits started to roll in, the administration had changed its argument, asking courts to uphold the law’s mandate as a valid exercise of taxing power.

Lower courts rejected that argument and at oral argument before the Supreme Court, even the chief justice seemed incredulous.

“You’re telling me they thought of it as a tax, they defended it on the tax power. Why didn’t they say it was a tax?” he asked Solicitor General Donald B. Verrilli Jr.

In his majority opinion, however, the chief justice embraced that argument.

“The Affordable Care Act’s requirement that certain individuals pay a financial penalty for not obtaining health insurance may reasonably be characterized as a tax. Because the Constitution permits such a tax, it is not our role to forbid it, or to pass upon its wisdom or fairness,” he wrote.

Paige Winfield Cunningham contributed to this report.