I don't know why you would, but don't go thinking that a government job will make you happy. It will not. I mean, maybe it will. I don't know your life. But I do know that tons of government workers hate their jobs, just like you.
Not at NASA: 73% of them like their jobs. But let's face it: they are astronauts. Or they get to help the astronauts. Are you qualified an astronaut? No. The chances of that are very low. It's far more likely that you're qualified to work for the Department of Homeland Security, where only 53% of employees like their jobs, probably because many of them are employed in airport security lines all day. Just think of what that would do to your overall mood.
The other least popular agencies are Veterans Affairs, Labor, Agriculture, Defense, and the Army, probably because all of them threaten to involve you in work that is hard and/ or hazardous to your mental and/ or physical health. Whereas the State Department and "Intelligence Community" are more popular, because you get to sit around talking about gossip a lot, which is called "intelligence."
In conclusion work pretty much sucks no matter who's writing the check, unless you're an astronaut and/ or spy.