“That was totally avoidable,” Mr. Zeldin said.

All told, 12 Republicans broke with their party line to vote no, including Representatives Dana Rohrabacher and Darrell Issa, both of California, and Walter Jones of North Carolina, who bemoaned the bill’s potential to add “trillions of dollars” to the national debt. “We’re going the wrong way fast,” he said in a statement.

But the opposition was by far the most concentrated in New Jersey and New York, two high-tax, largely Democratic states. And the chief source of consternation for Mr. King and others were new provisions to cap the combined deduction for state and local income tax and property taxes at $10,000. That limit, they warn, could decrease property values, stymie the real estate market and cause tax migration to less tax-heavy states.

“I don’t think there should be winner states and loser states,” said Representative Leonard Lance, Republican of New Jersey, who said that the combined $10,000 limit was simply too low for his state’s often expensive — and high-taxed — communities. “That’s not strong enough.”

Several of those who voted against the bill were probably also taking the current electoral calculus into consideration. Mr. Issa and Mr. Rohrabacher, for instance, are considered vulnerable incumbents heading into 2018, when Democrats feel an anti-Trump backlash could return the House to their control. In New York, Gov. Andrew M. Cuomo has repeatedly railed against the effect of the bill and promised to campaign against its supporters, calling them “Benedict Arnolds” and hypocrites, and predicting political doom if they vote yes. “I think there’s going to be a real political comeuppance,” Mr. Cuomo said Monday.

That sort of messaging was met by shrugs by many Republicans in New York. It also did not seem likely that the dozen defectors would face retaliation from inside the Republican conference. A few hours before the House vote, the chamber’s chief tax writer, Representative Kevin Brady of Texas, the chairman of the Ways and Means Committee, showed no ill will toward the dissenters.