He says he's hopeful that he, the Senate and House can reach a compromise on limiting some types of lawsuit damages.
The current special session was supposed to end at midnight tonight.
The effort to cap how much malpractice victims could collect for non-economic damages, such as pain and suffering, is meant to lower doctors' insurance rates.
The problem has pitted the governor against fellow Republicans, to the point where he has suggested donors not give money to some Republican senators.
Lawmakers have been working in special session on a measure that would limit pain and suffering damages but haven't been able to agree on an acceptable amount or details of how to do it.
Generally, Bush and the House have pushed for lower, stricter limits while the Senate has held out for higher caps with some exceptions for the worst-injured victims.