Quite simply, the statement Pace wrote here is a lie. It is totally false. If Congress refusees to raise the debt limit, it will not force a default in any way. Since, as Rob points out, interest on the debt is only $20 billion a month, and we take in $200 billion a month, it would simply force the administration to decide how to allocate the $180 billion that would remain. We would have 10 times the money we need to make our debt service payments.
Instead, Obama runs to the media and insists that this perfectly reasonable condition is the equivalent of Republicans asking him to cut off his left hand - and they report the news in exact synchronization with his preferred narrative.
He lies. They lie. And now a whole lot of Americans think that we'll default if the debt ceiling isn't raised, because they read that in an AP story that didn't quote anyone or attribute the statement to anyone. It simply stated it as fact. Which it is most assuredly not.