Well Obama was more vulnerable in 2012 then in 2008 (when the whole world was enamored with him- Remember the Nobel Peace Prize?) and Romney had a tough time squeaking through the primary. Seeing as Bush would compete with a lot of Romney's base (white collar, middle and upper-class fiscal conservatives/establishment types) it could have worked. Jeb Bush would have also had an easier time taking voters from more social conservatives in the further right Gingrich, ect. camps, due to having the Bush name on his resume. So yes, I could see him doing a successful campaign. The risk would be that he would merely split the establishment vote and funding with Romney and neither would be successful in getting the nomination.
I'm inclined to this line of thinking, myself, especially since basically every thread about the 2008 or 2012 election on the board results in a consensus of, "The Republicans do EVEN WORSE than OTL." Who knew our timeline was the best-case scenario for the Republicans in '08 and '12?

But I'll go one step further and say that I can see a way for him to do slightly better than Romney. Lots of pluses for Jeb in 2012 and one real downside. As mentioned, the Bush legacy means he's going to lose. But as badly as Romney? Points in his favor:
1) Romney had a long, drawn-out primary fight that made him look weak. Bush could potentially win with the 2012 GOP primary electorate simply with name recognition. No significant challenges mounted from upstart right-wingers fueled by voters who felt the party they supported from 2001-2009 was being abandoned. Sure, it's not a cake walk, but Bush will emerge as a consensus much earlier and wrap things up by Super Tuesday at the latest.
2) Romney had to juke fairly hard to the right to win over enough conservatives to counter his record as governor. Bush doesn't have to juke left or right, he just has to be a Bush. His record is sufficiently conservative for 2012 that he can stay vague in the primaries and moderate successfully in the general. He can campaign on the Gang of 8 immigration reform and can successfully attack Obamacare (unlike Romney, who signed MA's healthcare reform into law).
3) Romney had troubles among Christian conservatives that Bush simply wouldn't. Though neither are going to get those blue-collar Trump supporters to come out, which is going to doom them both.
4) 2012 is also much closer to Bush's time as governor, and the economy is still shaky enough in that state (in 2012) that voters still remember him with a rosy glow. And Florida is a swingy state. If nothing else, it means sinking more democratic campaign money into Florida.
But he's still a Bush. He's not going to win, but his defeat does result in a very different post mortem from the RNC. IOTL they said they needed to do better with Latino voters. Bush likely does okay with Latinos. So who do they go looking for? Do they correctly notice blue collar white men are their missing voters? Or maybe (and this is the dream) they decide it's moderates in general they're missing, as conservative votes just aren't there. Interesting possibilities.