WASHINGTON—A House committee began considering a bill Monday that would reduce taxes by $1.4 trillion over 10 years, but disagreements over key pieces of the measure could force the GOP to make changes and slow down plans to pass it by year’s end.

House Republicans are at odds over plans to eliminate deductions for state and local taxes. Senate Republicans disagree on child tax credits and whether to accept significantly bigger budget deficits. Narrow margins in both chambers leave the party little room to maneuver.

Here’s a look at the most significant fault lines that could make or break the GOP effort to rewrite the tax code:

Individual Deductions

The tax breaks for mortgage interest, state and local taxes and medical expenses are among the most popular in the tax code, and the House plan hits all of them.

State and local income and sales taxes and medical costs would no longer be deductible. Property-tax deductions would be capped at $10,000. The mortgage-interest deduction would no longer apply to interest on debt above $500,000, home-equity loans, or second homes.