
Any time you are paying some creditors but not others, you are in default. You may not be in technical default to the creditor you're paying, but you are "in default" in general.
An example: You decide to pay your home mortgage but not your phone bill (or you short-pay the phone bill, same difference). Because you are current with your mortgage-holder, they aren't able to foreclose on you (technical default), but you are in default on your debts, and obviously the phone company can stop your service.
The problem with the US government is that, unlike Joe Private Citizen, the mortgage-holder and the phone company (as well as everybody else) are aware of which bills you're paying and which you're not. Also unlike Joe, none of the US government debt is collateralized.
See, the mortgage-holder knows that, if you don't pay, they can take your house. This is not without risk to the mortgage-holder (house values may fall, you could trash the place before moving out) but there's some recourse. This is why mortgage interest rates are relatively low. The phone company, on the other hand, is not collateralized. All they can do is shut off service and hand the bill to a collection agency, while charging penalties. This is called unsecured debt, and this risk is why (unsecured) credit card debt comes at a high interest rate.
But again, none of the US debt is collateralized. It's all unsecured! Business 101 says that, if a creditor isn't paying one chuck of unsecured debt, all the unsecured debtors better go get their money now.
In short, any talk you hear that we can "prioritize payments" in the event we hit the debt ceiling is sheer ignorance. If we as a nation start prioritizing payments, we are in default. Every creditor knows that they may not get paid, and that they need to price that into any future lending decision.