I must have a tiny amount of a few of the traits that Eddie listed, because I admit to a smidgen of affinity for ole Newt. Shades of grey, folks.
Setting policy and governance opinions on Gingrich aside, if he and Obama went toe to toe in a debate on the issues, it would be a bloodletting on the order of Cheney-Edwards 2004. For all his cronyism and inside politics, Newt knows the Washington machine better than all but a handful of politicians. He's unstable and capricious, but when focused, he is formidable.
Obama? C'mon now. The single factor that most starkly separates Obama from Gingrich is context - Obama lacks it, and Gingrich has it many times over. By context, I mean that Obama can mention an issue, how important it is, mention it again, remind us how important...etc. Like him or hate him, Gingrich is adept at placing an issue in historical context, identifying the forces operating on the issue at the time, and commenting how it is relevant to modern policy. This is the academic in him. Having to explain complex things to college students over and over and over again has probably given him a very useful skill in politics. Obama's weakness is inexperience, and if Newt can go into his "professor mode" at a controlled pace, he really would make Obama look profoundly silly. Hell, didn't he even challenge Obama to a debate WITH teleprompter?
Don't misunderstand me, however. Although I enjoy listening to Gingrich, because he sometimes has insightful things to say, he isn't my choice for the GOP nomination because he's too risky. He still has too much of an uncontrolled academic style, and we academics are used to autonomy and shooting from the hip. When you have tenure and say something stupid, people just laugh at you. When you are running for president and say something stupid, you lose.
tl;dr: When you have a weak and vulnerable sitting president, you go with the safer opposition, and that's Romney. It may seem paradoxical, but strategically, IMO Newt would be a better opponent if Obama was popular.
