He will be irrelevant to the final outcome of the governor's race and has tarnished his image within the Republican party by not bowing out. The only thing saving him from an intra-party savaging is that his campaign fizzled and died about two or three weeks ago, eliminating the chance he could be an actual spoiler.
At this point, nobody cares what he does outside of his dwindling core of supporters and the liberals desperately hoping he can revive his candidacy to siphon off enough votes from Arnold to eke out a win for Bustamante.
That said, he will not be offered a position in Arnold's administration, nor would he accept one, because I think he is happy to remain in the State Senate for the time being.