Lawmakers head back to the state capitol Monday for a special session on redistricting.
Hearings have already begun on a bill to redesign the state's congressional districts.
The new plan would favor Republicans.
During the regular session, Democrats killed the redistricting bill by going to Oklahoma until a House deadline had passed.
The legislation likely would increase the number of Republican districts from 15 to 19, while decreasing the Democratic districts from 17 to 13.
U.S. House Majority Leader Tom DeLay has urged the Texas Legislature to redraw congressional lines to reflect the state's GOP majority.