The NSA is a 60 year old spy agency at the heart of the national security infrastructure and government.
You are comparing two entirely dissimilar things.
Also, how exactly is the American national security state 'weakened and vulnerable'?
At the moment, there are many people shouting for them to be shut down. Will it happen? Probably not. But at the moment, that is something for the NSA to worry about and to try to do damage control over. In that sense, they are certainly in a quite worse position.
The US Government operates on an extralegal basis (ie they're willing to cross any line), and roughly 85%+ of all new debt is purchased by the Federal Reserve. What very specifically is not going to happen, is the shut down of the military industrial complex of which the NSA is such an integral part.
So long as the dollar (Federal Reserve Note I should say) remains the global reserve currency, the national debt is a trivial problem (as is paying the interest on it). The dollar is the real linchpin, to everything. All else is a sideshow of political gamesmanship.
If a credit card company refuses to raise your limit, that is not a default. A default is when you stop making payments on your debt. As long as the government has enough tax income to pay interest on its debt, there is no default. Calling it a default is a scare tactic to get their credit card limit raised.
The solution is for governments to spend only the tax revenue they receive - no more. Not only should the debt ceiling not be raised, it should be slowly lowered to zero over the next 10 years. If the government had to explain to everyone how much their taxes would need to be raised in order to invade Syria, etc., people might actually pay attention. Just my opinion.
If the US wanted to instantly achieve a balanced budget, they would have to spend 3/5ths the current amount. When a government cuts the amount it spends, it shrinks the economy, and reduces tax take.
In the UK, a limited form of this strategy seems to be working, but in Southern Europe, a strong 'austerity' strategy is creating a spiral of reducing tax take (requiring ever greater cuts).
So the sharp reduction in the deficit you mention is not possible. It would need to be gradual.
The elephant in the room is that, in the US, China, and Europe, the aging population is coming. As the proportion of contributors to consumers of public spending shifts, more debt is inevitable. It's going to suck pretty bad for everyone, but if we (all of us) can't achieve a balanced budget before that hits, then things are not going to be as gentle.
Currently government isn't able to pass a "normal budget" much less a very radically changed budget + huge and rapid changes in government agencies - if USA doesn't rise the debt ceiling, the actual effect will be not paying the interest due which is called a default.