It doesn't matter what the White House agreed to and even if it passes in law it would take a Constitutional Amendment to strip the President's Authority. I would bet that it merely sets a time restriction on the WH to authorize the action and anything after that has to go to FISA.
Bush isn't going to stop doing what is necessary...he is just pacifying the baby politicians that have their feelings hurt.
By doing THAT, he IS doing his constitutionally mandated job...keeping our country safe.
To hell with the Congress and their lust for power and attention.