House Republicans had planned to use a second phase of tax cuts to force Democrats into a difficult vote ahead of the midterm election. Now party leaders may drop the effort, fearing it could backfire by antagonizing voters in some hotly contested congressional districts.

The proposal would make permanent the individual changes in last year’s overhaul — including the $10,000 annual cap on the federal income tax deduction for paying state and local taxes, one of the law’s most disputed provisions. That would put Republican lawmakers in high-tax states such as California, New York and New Jersey in the tricky position of either supporting the cap or voting against tax cuts backed by their party.