Senator Clinton would have had the nomination. She almost had it in OTL despite Obama running.
Senator Clinton essentially had everything wrapped up from the get go, and in fact, that's part of what led to her downfall, because she didn't bother to run a campaign until after Super Tuesday. Up until then she and everyone else assumed she was going to be the nominee, and it wasn't until Obama showed everyone up by demonstrating he could run an extremely good campaign that Senator Clinton buckled down and focused.
And really, that ended up being possibly the best vetting process Obama could have gone through. Everything that could have been dragged up, from Reverend Wright, to Bill Ayers, allegedly being a Muslim, his "inexperience" and so on and so forth, all were brought up during the knock-down dragged out fight, and all were demonstrated to be what they were.
Now McCain trying to use these tactics is finding they're not very effective, and not just because the economy is so central to everyone's concerns right now, but also because they were already shown to be what they are: untrue, worthless accusations.
I do believe, however, that had Obama either failed to win the nomination or did not run at all, Senator Clinton would have lost any potential race for the Presidency. She has simply far too many skeletons in her family closet, her own reputation--she is literally hated by a significant number of Republicans--and the fact that she wouldn't have adopted the fifty state strategy that Obama is using. Obama's strategy not only challenges his opponents in battleground states, but everywhere, and as a result, has demonstrably shown serious changes in demographics. We have the possibility of states like North Carolina--NORTH CAROLINA--going Democratic this year, because of his strategies.
Senator Clinton would have focused on the same old +1 strategy of focus on your base, and then grab undecideds and Independents, and we would see another Republican President. (And, for that matter, we wouldn't see an energized youth voting populace. Obama's strategy has also registered enormous numbers of new voters and gotten an entire new generation energized and interested in politics rather than apathetic. That's one of the many reasons I hope he wins, because I don't want that to disappear--or worse, suffer a backlash--as it surely would if McCain were to win.)