The plan increases the share of Hispanic voters in three of the five districts targeted by the GOP, banking that enough will turn out and vote for Republicans without Donald Trump on the ballot.

The proposal would redraw district lines in ways that target current Democratic members of Congress in districts in South Texas and around Austin, Dallas and Houston.

The full Texas House will now vote next week on a map drawn to flip five House districts to the G.O.P., but Democrats might walk out to deny Republicans a quorum.