What I would prioritise:
(I am addressing the American government as "you" for the sake of simplicity)
1) I agree: balance your god damned budget. If Bill Clinton was able to preserve frontline public services with low spending, any other President should be able to do the same. America's debt is 97% of GDP, which does not even approach being sustainable. How should you reduce it?
2) Cut healthcare spending. There is seriously no excuse to be spending close to $2 trillion on the level of nationalised healthcare that the USA provides. If you want a proper health service, go all the way like Scandinavia or, hell, even like Britain. If you don't, don't try to find this absurd middle ground where you spend the money for none of the benefit.
3) Get people working again. 9.6% unemployment is very troubling. Cut corporation tax and incentivise entrepreneurship. Your companies cannot deal with the enormous American work force. Hell, start ambitious development projects if you like. Just get people off state pensions and food stamps and into work.
4) Stop fighting pointless wars; they are a waste of money. I should add that Afghanistan is not a pointless war. Iraq, on the other hand, is a pointless war. I know that the official government view is that the USA has pulled out of Iraq, but I don't call leaving 50,000 armed troops in the country "pulling out". The Iraqi security forces are strong enough to take care of themselves. They are no longer your responsibility.
5) Whatever you do, do not abolish political parties. If I go into the voting booth and see Fred Smith, Joan Green, Phillip Blake and Steven Jones on a ballot paper (I, in this case, being the average citizen of any country in the world), I have no idea who the hell they are. Voter turnout will drop enormously. But that's not even the real problem. If anything, that's an advantage.
The problem ties in with a similar suggestion of mine: do not ever try to form a third party. Government efficiency will become a distant dream. The House of Representatives will refuse to ever work together to get anything done. They will constantly bicker about slightly different interpretations of inane issues with the result that very few laws actually get passed. Thanks to the separation of powers and the superiority of the Constitution, laws hardly ever get passed anyway.