The maps achieve a five-seat swing largely by shaving slivers of Republican strongholds from ruby red districts and placing them inside three urban districts.

The first draft of the lower chamber’s new redistricting map targets Democratic members of Congress in the Austin, Dallas and Houston metro areas and in South Texas.

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.