The effect isn't instantaneous. A number of government institutions have emergency funds for exactly this sort of occurrence. For instance, the Supreme Court can operate for two weeks without being budgeted. Others, which operate off of money from fees, not taxes, will never be affected directly. Hence Immigration hasn't shut down.

In general, this whole little escapade is being seen for what it is... a temper tantrum by the Tea Party. Sad to see the GOP go out like this, but go out, it will... their approval ratings have taken the biggest hit, and they didn't have much going for them to begin with. Obama's hit won't affect reelection, the Dems are looking to pick up seats...

Oh, and American faith in the government is being crapped on by people who ran for office in order to crap on it, so well done by them, I guess? It just goes to show why anti-government types should be banned from running for office... there is a distinct conflict of interest, and they'd all rather serve a term or two and then make money on the speech circuit than serve their country.