It could have an effect in a Republican primary race for governor. First, it’s never good to get beat, and having to withdraw to avoid the embarrassment of a defeat is getting beat. Maybe that will be forgotten by March 2010, but the other problem is that one reason she withdrew from the race for chair of the Republican Conference is that conservatives turned against her. (The other reason is the likelihood that she will leave the Senate to run for governor.) The perception that she isn’t conservative enough has dogged her ever since she lost a bitter race for a Dallas congressional seat to Steve Bartlett in 1982, after having the lead going into the runoff.
Hutchison has a large reservoir of personal popularity to fall back on. When she was considering a challenge to Rick Perry for governor in 2006, she took a couple of polls in the spring of 2005 of likely Republican primary voters. The first poll came back Hutchison 58 Perry 33. The second poll came back Hutchison 58 Perry 34. She was ahead with every group of voters, including hardcore pro-life voters. I don’t think the leadership race will have an impact three years from now, but an opponent might be able to get a TV ad out of news stories in which some colleagues questioned her conservative credentials.