The greatest affect this would have on OTL events would be the 111th Congress bills (Obamacare, Stimulus, etc.). Dole would deny Democrats a filibuster proof majority, even with Specter's switch. The Democrats could have tried to court Snowe to at least become an Independent, though I doubt she would have. Maybe the filibusters would be nuked? Later, I can see Dole retiring in 2014 after her second term, and handing off the seat to Tillis in the midterm year. Without the Democratic nominee having the incumbency advantage, Tillis would win by a larger margin than he did IRL.
I'd think maybe either Lieutenant Governor Forest would run or one of Paul Coble or Tom Fetzer. I really doubt Tillis would win the primary.