WASHINGTON—Republicans disagreed with the White House over tax treatment of 401(k) plans and sought to resolve differences over state and local taxes on the eve of a House vote that is crucial to their tax-cutting ambitions.

The jostling showed the challenge the party faces as House lawmakers prepare to lay out the fine print next week of their planned tax overhaul. Republicans have made public broad plans to reduce individual and corporate tax rates, but have left out many knotty details over who wins and who loses, and which...