The consequences of a default by the US on its debt, even if temporary, are so profound that it is unthinkable that Congress would allow such a thing to happen purely because they think they can overrule the electorate who in electing President Obama for a 2nd term last November showed clearly what the people want.
Public opinion of Congress is rock bottom. If they let the country default they would be signing their suicide note.
Rational thinking would suggest that the House GOP will soon have a Berlusconi moment and back down even if Obama is gentle enough to offer a face saver by entering negotiations on further measures to cut the deficit which is in any case falling on its own momentum.
But can you expect rationality from the irrational?