Why can't they use super computers to mine all the bitcoins? I have very limited knowledge of bitcoin, but, I hope you don't mind my asking this question:

As I understand it, "mining bitcoin" requires "significant" computational prowess. A lot of dedicated mining rigs have been built out of FPGAs, ASICs and GPUs. But, I have always wondered: would it not be possible to mine ALL the bitcoins if you had access to some of the most powerful computers? So, for argument sake, if the NSA decided to stop snooping upon people and instead decided to, you know, mine bitcoins… would they be able to mine all the bitcoins in just a few hours if they redirected all their super-computational-power towards this one problem: mining bitcoins? Other potential candidates for this game include, but are not limited to: NASA, DoE, etc.

I realize that running a supercomputer to mine bitcoins may NOT be efficient (because a super computer consumes too much power, costs a lot of money, etc) but for a govt agency all that money comes from taxes so ... 

Now, hypothetically, could "they" mine all the bitcoins in a few hours, or even in a few minutes if they redirected all their super-computational-power towards this one problem: mining bitcoins?
A supercomputer is way slower than mining with ASICs. A supercomputer only has much CPU power, not even GPU power and ASICs are way more powerfull than GPUs. ASICs represent the hashing algorithm as hardware which means they can't do anything else, that's why they are so fast.

At http://bitcoinwatch.com/ you can see the current network hashrate in PetaFLOPS, which is 1534782.24 at the moment. Currently the fastes Supercomputer Tianhe-2 has 33.86 petaFLOPS.


  but for a govt agency all that money comes from taxes so ...


If they would use all the money to buy ASICs and start mining bitcoins, it still would not be enough because of the difficulty factor. But they would be able to get a lot of blocks because the difficulty only changes every 2016 blocks.