This sounds good. It is good. But it isn’t as good as it sounds.
It’s also a gimmick. In Obama’s defense, it’s a gimmick that others have used.
The problem is that the “budget”, as defined here, is not the whole budget but just the discretionary part. This is the portion that Congress can change just by passing a bill that changes a dollar value.
Unfortunately, there are also parts of the budget that are non-discretionary. These are areas where there is some formula determining payments, and that formula is not so easy to change (not impossible, just difficult and unlikely).
For example, discretionary spending is something like disaster aid for Haiti. Non-discretionary spending is something like cost of living adjustments (COLA) to social security checks (these are tied to the CPI).
The reason this freeze is not as good as it sounds, is that only about 1/6 of the budget is discretionary. The other 5/6 will increase because the laws governing it include automatic increases that don’t require anyone’s approval.