It's the Republicans who will cave in on this, not Obama.
There are also two types of defaults, which are repudiation and monetization. The former pays the creditors nothing, revalues the dollar, and lets the people off the hook, while the latter destroys the dollar and barely gives anything to the creditors.
If I were in Congress, I'd be telling everyone that we need to repudiate it, that by doing so they'd be let off the hook, and that unemployment would be at historic lows 6 months from now. Also, no one would loan anyone another dime.
However, that's just a fucking pipe dream, because in the case of default they wouldn't repudiate it, they'd monetize it because Congress just fucking loves inflation and they want to destroy society.