WASHINGTON — Republican leaders are backing away from a proposal to fully repeal an expensive tax break used by more than 40 million tax filers to deduct state and local taxes amid pushback from fellow lawmakers whose residents rely on the popular provision.

The state and local tax deduction is estimated to cost $1.3 trillion over the next decade and its repeal is central to paying for a sweeping tax rewrite unveiled last week by Republican lawmakers and administration officials. But elimination of the provision has emerged as a flash point in the nascent debate over the plan, with Republicans in high-tax states worried about backlash from residents who could see their tax bills rise.

The White House and Republican lawmakers are considering alternatives to an outright repeal, including allowing taxpayers to choose between deducting their mortgage interest or state and local taxes, a limit on the deduction or a special tax break for middle-class families that live in areas with high property taxes.

Representative Chris Collins, Republican of New York, said in an interview on Tuesday that party leaders had assured him “there’s not going to be full repeal” of the state and local tax deduction. Mr. Collins, who represents a district in upstate New York, is among the more than 30 Republicans whose residents make heavy use of the deduction and would be more likely to see their tax bills rise if the provision is eliminated.