As for the military not being paid. hogwash.
Three ways this can happen. they can get support from the Veterans association. The Deers program. Or a neat little thing called "backpay".
The deers program is a likely scenario due to the fact that it pays an extra amount of money per paycheck to enlisted and officers of just about all branches of military to supplement the income and upkeep of family living stateside. The most likely scenario is the back pay system, where they go without pay for any amount of time and eventually when funds are made available they will be paid in full on payday every dime that they were owed. Landlords and landowners will generally not mind not being paid if an extend on the bills are requested due to the government not paying its armed forces, because eventually a budget would be settled upon and they would likely be paid off in full anyway. The deers program is paid into by every member of the armed forces ( if i recall correctly) since day one of starting their career. Families or not. (thats how the program is made possible. There may be other ways they are supported but none come to mind and i cba to cite any sources considering we have handy dandy google.)
As for the whole two party system here in America, Its actually not a two party system but people thinking it is, due to ignorance and the fact that the media only cares to cover the two parties and not any of the other ones really in my observations is all behind the whole thought process of that notion.
As for the debt ceiling not being raised and such, i don't see it effective to shut down the government while the politicians are STILL getting a paycheck. Take that paycheck away and watch how fast they fold. I can't be the only one who has thought about that. The government is no longer for the people. The government isn't shut down if the guys running things are still running them and getting paid to do so.
That much is certain.