WASHINGTON—Republicans, long champions of tax cuts for higher earners, are conflicted in just how far their latest plan should go in reducing the amount paid by the rich.

The party’s tax-plan framework, unveiled this past week, jettisoned some tax cuts Republicans have long supported for high-income households, leaving rates on capital gains and dividends untouched. The party also has shown an openness to keep the top tax rate for individuals near its present level of 39.6% and has proposed to cut deductions on state and local...