As I mentioned this morning and in my recent piece, not everyone in the administration was enthusiastic about the freeze idea from the get-go. Some were concerned about shifting to deficit-reduction mode too quickly, while job-growth was still a big problem. (The National Economic Council, for one, was initially pretty skeptical.)
At the same time, some in the administration who worried about the deficit didn't see the freeze as a huge help in that regard. Here's a quote from a senior administration official I talked to shortly after the idea trickled out which reflected that view: "They're being hard-asses, which is appropriate," this person said of OMB. "But it doesn't move the needle. The money is in entitlements, and defense, interest payments." (On the other hand, as I note in the piece, the point of the freeze isn't necessarily to move the needle today, but to buy a little time before the needle has to get moved.)
For what it's worth, my understanding is that no one really dug in on this--everyone outside OMB understood the importance of beginning to think and talk about reining in the deficit; and OMB itself understood the importance of not stepping on the recovery at a still-fragile moment. The differences were basically differences in emphasis, and so they weren't that hard to work out.