This is the subject of my new piece, right here.
There are three likely outcomes. One: America defaults on its debt, and all of the nightmarish things Treasury Secretary Timothy Geithner is predicting actually happen , with Republicans taking blame. Two: The debt ceiling is raised, with Republicans getting mostly toothless concessions. Three: The debt ceiling is raised without concessions, but with Democrats providing the margin of victory, a critical hit to House Speaker John Boehner's machismo.
Worth reading: Sam Stein on how the White House isn't exactly adamant anymore about a "clean bill."