Aside from the obvious—he wants to go to Washington—I can’t think of a good reason to run for Senate instead of governor.
As things now stand, Hutchison will probably resign her seat in the fall. I believe that Perry will appoint either David Dewhurst or Greg Abbott. Michael Williams would be an interesting choice, but Dewhurst or Abbott should be able to hold the seat in a special election, which would take place in May. Williams would not be a sure thing.
Can White defeat either Dewhurst or Abbott in a special election (no primary, just the top two vote-getters in a runoff)? I don’t see it. Either Dewhurst or Abbott will be able to raise a lot of money. Dewhurst can put his own money into the race. Abbot has been a very successful fundraiser. White can spend personal money as well, but he will be facing an incumbent appointee who has been able to raise money in Washington as an incumbent for six or seven months. Democrats generally do not turn out for special elections as well as Republicans do. That is not good for White either.
On the other hand, suppose that White runs for governor. The Republican nominee will be the survivor of a brutal primary. If the nominee is Rick Perry, he is vulnerable in a general election context. And if it is Hutchison, well, she looked invincible when the first polls came out, but she doesn’t look so strong today. Democrats will be excited about the chance to win a statewide election for the first time since 1994. If White wants to win, he should run for governor.