At one point during the debate, Romney nailed this precisely by noting that the details of tax policy are something that Congress hammers out. The president has some enormous powers in the legislative process, but they're powers of agenda-setting and the ability to veto—not at all the power to delve deep into details. And indeed I'd say President Obama ended up having a lot of problems with his base that could have been avoided had not Candidate Obama made so many specific pledges that he had no real way to deliver on.I get what he's saying, but I think this is wrong from the point of view of both Romney's party and, perhaps, ordinary voters.
Rather than demanding more specifics, what I wish is that reporters would press candidates for more clarity...In general, though, this kind of way of talking about things—what won't you do, rather than what will you do—makes a lot of sense as way for presidents to talk about their agenda.
For party actors, at least for those with policy preferences, the game is to constrain party politicians as much as possible. It's true that presidents have limited control over the fine point details of legislation, but that doesn't mean they have no influence at all. That's obviously true for interest groups as well. Suppose that you're the Realtors, for example; you really want candidate Romney to commit to leaving the home mortgage interest deduction out of any potential tax reform, or at least to stay quiet on it in the hopes they can win on the Hill; they really don't want him to indicate he's for scaling back or eliminating it.
What about for ordinary voters. They, too, have an interest in politicians including presidents promising what they want to do -- because the press and the opposition will probably pay more attention to it during the campaign than they will after the election, except in rare high-profile cases. Say that Romney wants to slash spending on Obscure Program. It's eventually going to come down to the House and Senate Appropriations Committees or, perhaps, Ways and Means and Senate Finance, where it will be lost in the media shuffle most likely. But if the presidential candidate commits to it before the election, then opponents will know to mobilize, and proponents will too -- even if the president's actual role in the fight in those committees is marginal or nothing.
Now, for the president, being unconstrained by policy commitments is almost always a good thing. The only exception is the extent to which the president can claim a mandate if an issue was discussed on the campaign trail, but it's not at all clear what that gets presidents anyway, and of course they can always claim something as part of their mandate regardless.
So, yes, it's probably right that Obama had problems he might not have had if he had been less forthcoming earlier...but he also probably did things that party actors wanted which he might not have otherwise done.
Promises are good for representation, good for parties, but constraint politicians. And so everyone but the politicians should be pressing for them.