“This is the kind of routine modifications or tweaks to a large program that’s starting off that in normal times in a normal political atmosphere would draw a yawn from everybody,” Mr. Obama said. “The fact that something like this generates a frenzy on Republicans is consistent with the fact that they’ve voted to repeal this thing 38 times without offering an alternative that is plausible.”

Mr. Obama said members of Congress who questioned his power to delay the provision should “make that case.” But he pointedly suggested that the criticism had less to do with the substance of the issue and more to do with political efforts to undermine his presidency.

“There’s not an action that I take that you don’t have some folks in Congress who say that I’m usurping my authority,” Mr. Obama said in the interview. “Some of those folks think I usurp my authority by having the gall to win the presidency. And I don’t think that’s a secret.”