On that I would definitely agree; and in fact you don't have to even freeze them! Simply pegging them to inflation plus population growth would solve the deficit AND the debt!
I wrote a small article about the facts of the situation that show a fixed budget that grows annually at a reasonable rate (to allow for increasing costs via inflation and increasing users via population growth) will grow over the long term slower than the GDP, meaning that tax receipts will soon outstrip the budget and allow us to work down the debt.
I think it's a common sense approach that would be politically viable; a complete freeze would never work unless you had a 60% majority in the Senate, and the GOP has NEVER had that luxury. Force the Democrats to explain why the budget must increase faster than real-world costs require; that's a losing argument for them. And it does not allow the charge of "hurting women and children" against the GOP since not a single budget item is touched. if you make such charge, then implicitly you're admitting that the previous years you WERE hurting women and children!
I've asked about this plan on previous Tea Party revolt threads and been told I was a RINO and sell-out since I wasn't for cutting the Government; yet if you actually understand the plan you see that over the longer term the Government IS necessarily cut! It shrinks - rapidly, near the end I might add - as a percentage of the GDP which is a good thing in limiting its power. But then again, it does require compromise and that is a dirty word for many Tea Party folks.
Some aspects of the federal government budget will need to grow at a faster rate at certain times. This I think is where your plan gets weak. Someone needs to be willing to make an exception now and then and have the balls to cut something else to offset the exception. This is where all the political fighting and whining is going to come about. Everyone will want to be the guy that gets the exception for his pet program.