“As Republicans, generally tax cuts are the one thing we can all agree on,” said Mike DuHaime, a Republican strategist in New Jersey. “I think the leadership in Washington has been misguided on this in terms of having this approach that hurts certain states — New York, New Jersey, California, Maryland. You have a lot of representatives in these states that are hurt by this.”

Brigid Harrison, a professor of political science and law at Montclair State University in New Jersey, said the decision to hold the vote “tied the hands” of some Republican candidates.

“This is kind of the politics of both class and geography playing out in these competitive districts. It’s a battle for who is the Republican Party,” Professor Harrison said. “Is it the Republican Party relatively in the Midwest and the South not burdened by high property taxes, or is it some of these more affluent northeastern states and California?”

Democrats have wasted no time seizing the opportunity.

In New Jersey, Mikie Sherrill, who is competing against Mr. Webber for the seat in the northern suburbs, took to social media and sent emails announcing that “Washington Republicans are seeking to punish New Jersey taxpayers.”

Tom Malinowski, a Democrat who is challenging Republican Representative Leonard Lance in the western part of New Jersey, weaves the tax issue into nearly every speech.

“Their top priority right now,” Mr. Malinowski said of the Republicans at a campaign stop where he was endorsed by the Amalgamated Transit Union, “is making the tax reform bill that they passed last year permanent. That’s their priority. None of them are talking about an infrastructure bill.”