(promoted from an overlong comment)
There's a fundamental misreading of what Americans really want in leaders. The railing against "career politicians" isn't so much, really, disinterest in people who have ample experience, it's a dislike of people who have lost touch with the real life issues everybody faces.
Romney is running on a resume, of sorts, and IMHO it's a thin resume (a decade and a half as a 'businessman'/financier, four years as governor of a mid-sized state, and about 20 years of running for offices more or less full-time). But it is not the sum total of his life experiences. I would actually grant that Romney is more of a whole person than his silver-spooned resume would indicate.
That said, what attracted many of us to Obama in the first place was understanding he had an extremely rich, complex, and close to the ground life history. More thoughts on the flip.
While not exactly growing up in poverty, Obama had great logistical difficulties of the working family to deal with: short money, short time, difficulties of educational opportunities, a mother who strove to do better but also provide for her children. Getting ahead while getting by.
He lived as an outcast in his own home, as an outcast in a foreign country. His parents came from almost irreconciliably different backgrounds, and he struggled with an absent father. He had brilliant gifts, but chose, after tasting life on Wall Street, to move into community service and thence into law (and not the seven-figure partnership kind of law). (Let's face it, as editor of the Harvard Review, he would have had his pick of legal jobs had he chosen to go the Armani route). He had experiences unlike most of ours, to be sure, but he also had a basic life that was undeniably very close to that of the average American in terms of both struggles and rewards. He admits he was lucky, but of course talent and hard work played far bigger roles.
I note, parenthetically, the personal attacks on Obama have not just attacked his otherness, but the very idea he earned his place at the podium by his own efforts. Yeah, Bill Ayers wrote "Dreams of My Father," the smears go. He got into Harvard Law because of affirmative action. He only got to be President because he was, um, popular. Blah blah blah. All this was and is an attempt to undercut the incredible value of Obama's life experience in forming a wise person, someone capable of making good decisions in an extremely complex role.
The problem with Romney is that his kind of suspect, padded resume is not informed by real struggle. The fact of his wealth is well-known; even George W. Bush, with all his Daddy's buddies bankrolling his oil and baseball business ventures, not even to mention government subsidies supporting both businesses, had to go through rejection and bankruptcy. Romney simply hasn't failed, and it isn't because of any evidence of his brilliance. He hasn't failed because he hasn't taken any real risks with his life. He hasn't quit a cushy job to go work on the streets of Chicago. He didn't reject the six-figure salary out of law school to go teach, and he certainly didn't have student loans into his 30s and a mortgage in his 40s. His overseas adventures were spent in a Western democracy, living in comfort, in his 20s, not (ahem) eating dog in a rough section of town as an 8 year old. Whe he is asked to think of a situation where he overcame adversity, his response is to cite a novel solution to the problem of an overpacked car.
Life experience does count. I do believe that experience in government and public service counts for part of this, although it is neither sufficient nor necessary all by itself. Executive management, and the kind of leadership we require from our President in this day and age, requires a bigger set of skills, a deeper way of seeing, a more intimate knowledge of risk and failure and reward than you get either by running a small financing company or serving part of a term in the Senate.
And frankly, Obama has really ably earned the initial trust many of us gave him on the "3 AM phone call" issue. In 2008 we had to go with a bit of intuition about him -- evidence he was against the war in Iraq while most of his Democratic colleagues were against for it and a few other issues were only an indicator of his decision-making ability, not a thorough vetting of his abilities. But without getting into the numerous examples, it is the reality that he faced an incredibly severe economic crisis and complex, if not existential, problems overseas with a great deal of aplomb.
When W. ran for re-election, many of my more conservative friends and relatives used the mantra "you don't change a horse in mid-stream". Ignoring the fact that this particular horse was already in over his head, anc changing the horse would have been a good way to avoid risking of drowning, the argument was that when you had somebody who (supposedly) had done OK, you were better off sticking with that person than risking a change.
I never bought the simplification of that argument, but if it was ever valid, it is now. The President has done an excellent job of wading turbulent waters. There's nothing on the Romney resume that makes me think he could do better, even completely ignoring the issues (at our peril, of course) or the question of the Parties' different visions for America and liberty. And there's even less in his life experience to make me think Romney has the wisdom that is so much more critical than the conventional experience, per se.
(Update 1: minor typo edit.)