As I said yesterday, I don't think it's a mistake at all to try to regard change in White House personnel, especially the Chief of Staff, as a big deal. How well the White House runs can have a lot to do with whether presidents succeed or not.
I'll add one general thing about the kinds of speculation we see in these situations, and one specific thing about Pete Rouse. The general thing is that far too much is made of ideological leanings. I think that's usually true even of the president himself -- the president's ideological or even issue preferences are often a lot less important in determining what he does than the demands that various constituencies place on him, combined with his political context. But it's even less true of presidential staff -- especially within the Presidential Branch. People who work in the White House work very directly for the president, and while they do his preferences are theirs. Sure, around the margins it might make some difference, but I wouldn't be very confident about that.
Now, as far as Pete Rouse...from what we know he has several strengths for the job: he's a problem-solver, he doesn't cultivate enemies, he knows the Washington landscape well, he has an excellent working relationship with the president. My immediate concern about him, however, and it's significant enough that I suspect Barack Obama would be better off moving elsewhere for a longer-term solution to the CoS opening, is that his experience is apt to give him too much of a Hill focus, when he's working for an administration that has generally been at its weakest when it comes to managing the executive branch. Whether it's the war in Afghanistan, or the economy, or implementing the ACA, the real challenges and the real fights over the next couple years are far more likely to be found in executive branch agencies and departments than in the House and the Senate. Climate, too. Of course, managing relations with Congress will be important, especially, I would guess, for budget politics, but regardless of what happens on election day this year we know that major legislative initiatives (outside of the budget) are just not very likely.
Of course, it's certainly possible that Rouse will overcome his background and do a great job in that regard. But it's been a weakness of this administration from the beginning, and my guess would be that elevating Rouse is a symptom of it, not a step towards a cure.