'broke' no the US Government is able to pay its obligations. US debt is the fifth safety of 156 countries. Tax revenue as a percentage of the economy is at a 60 year low so there is room to raise taxes as California did.
Alexander Hamilton,1st Secretary of the Tresaury, in 1790 absorded all of the States war debt. He had no intention of paying it off, rather he made regular payments on the interest establishing the US as a primier payor of debt obligations.
'Debts exceeding income is not broke' George Bush Administration.
What the Tea Party, as expressed by Ted Cruz and Rand Paul, want is to break from Hamilton's formual and cause wide spread market panic and a crash. Sort of like the Taliban of economics. Create a chaos by terrorism which in this case would be defaulting on our obligations. Cruz should be arrested if it comes to that.
Countries do however payoff enormous debt. Germany paid the US for the WWII war debt sometime in the late 1990s. Germany is still successful and they have an excellent Universal Health Care System.