There's a lot of variables at play here that would determine whether or not ATL Obama would even be interested in a political career. Lets assume he is; maybe a late POD is that he goes back to Hawaii after Harvard Law for a position at the University of Hawaii Law School. That keeps everything in his life the same, including community organizing experience in Chicago, up until 1992. The Senate seats in Hawaii were pretty locked down between Akaka and Inoyue (both Democrats) until 2012. House seats are available in this time period, but that's not a good launching pad for national office. If Obama has to wait around for Akaka and Inoyue that means a seriously delayed entry into high-level national politics. The governorship is an option; there was an open seat in OTL in 2002, which was won (barely) by Republican Linda Lingle, due to the Democratic Party being scandal-plagued (Lingle was popular and won big in 2006; her Senate campaign later on was a complete failure, which just shows you that people care more about party when voting for national rather than state office). If Obama can win the governorship in 2002 (not unreasonable), and runs for President in 2008- I don't think being a small state governor hurts him with primary voters per se. Howard Dean got serious consideration in 2004 despite governing a state with only three electoral votes. However, what launched Obama to national prominence was his speech at the 2004 Democratic Convention. He was given a prime speaking slot because the party leaders saw a charismatic young Senator as a rising star. If he's just the charismatic and popular Governor of a small and very out of the way state, then he may never be given that opportunity.
Long story short, even assuming Obama is still interested in politics, Hawaii is a poor launching pad. His entry into high level national politics would at the very least be seriously delayed.