Now let's translate that into English. All sorts of financial institutions fund their day-to-day operations with ultra-short-term borrowing. Repurchase agreements (or "repo") are the most common type. Here's how it works. A bank "sells" something for cash, but agrees to buy it back at the end of the day -- hence, repurchase -- for a little more than it got. So, for example, say a bank sells a Treasury bond for 95 cents on the dollar, and buys it back for 96 cents at the end of the day. Again, notice the difference between what it gets and what it pays for the collateral. That's the interest rate on what is really a secured loan. Okay, but what does this have to do with the debt ceiling? Well, the repo market isn't set up to tell if a Treasury bond has defaulted or not (because if Treasury bonds are defaulting, the world must be ending, right?). That means it only takes the hint of the possibility of a Treasury bond defaulting for the repo market to go into paroxysms. As you can see in the chart below, via Cardiff Garcia of FT Alphaville, that's exactly what happened during the last debt ceiling crisis in 2011: repo rates spiked when it looked like the debt ceiling wasn't going to be lifted in time. It'd obviously be worse if it actually wasn't lifted in time.

In other words, interest rates would rise for financial institutions. And those financial institutions might not get as much help from the Fed as they need. The central bank's clearing system also isn't set up to tell if a Treasury bond has defaulted or not, so it could seize up too. And, of course, banks can't use defaulted Treasury bonds as collateral at the Fed.
These are all very bad things.
So, to sum up, if everything goes as well as it could, the recovery would only get a vicious knee-capping. There'd be the insane austerity. Interest rates would fall for the government, but rise for the financial system. And households would be scared for months, if not longer, about a political system exhibiting what my colleague James Fallows calls 1860s-style dysfunction.
Scenario #2: Treasury can't prioritize the debt, and the world really ends. It sounds so easy to pay the debt back first. But prioritization is a legal and logistical nightmare. There's just little legal basis to justify paying some bills, and not others. Everyone we owe money to -- bondholders, military personnel, Social Security recipients, etc. -- has a good claim on whatever money we do have. Good luck getting whoever we stiff to go along with that.
But even if we could legally choose who and who not to pay, we might not be able to do so technically. As BPC points out, the Treasury makes 100 million payments a month. It would have to reprogram its computers to pay the most essential ones first each day -- and it would have to do this fast. It's touching that Republicans so believe in the efficacy of government that they think the Treasury could pull this off without a hitch. But I'm not so sure.