Rather than judging Presidents based on how their policies match with my own personal political ideologies, I prefer to judge them on how well I can see them performing their role in the office. This past election was past from clean, and as far as I can see, the Republican reaction to the election has not left President Obama with a Congress easy to work with. Since there's a split Congress, if Romney had won, he still would have had trouble with the Senate. However, with Obama's heavy influence on compromise for his past term, I feel like Democrats would be more likely to comprise with Romney than Republicans with Obama, even if they only do so out of an obligation to uphold their image as 'cooperative.' Romney, if nothing else, has also shown his flexibility in policies. While this has disgusted some people, I feel we need a President who knows how to do this. The current public image of the relationship between the President's seat and Congress is one of constant fighting. Certainly, both parties would like to paint it this way, because it's beneficial to both to show their side "extending the open hand of compromise", while implying it's the fault of the other side for being stubborn. Romney, hypothetically, would more easily be able to reach compromises and successfully push for bills because of both his flexibility and a more open Congress. This would give the public a more positive image of the government and increase faith that, perhaps, the government isn't broken and can still get things done. This faith, more than any policy a President can push, is what I believe can aid the country most at this point.
While I agree that Romney might have been able to pull off more compromises, I don't think that faith in government is more important than reasonable policies, which Romney really didn't have any of. I would go so far as to say that it's far preferable to have a government that accomplishes nothing than one that changes things in a negative direction, e.g. cutting health care, obfuscation of budget plans, necessary tax hikes falling on the poor and middle class instead of the rich, etc. In fact, given current Republican willingness to put this country on the line for corporations and the upper class, I would be happy to see a presidential term with no negative change. The positive change can happen once the Tea Party representatives are gone; for now, just hold the line.