The republicans complain about what they don't like in the stimulus bill. First it was contraceptives, then it was fixes to the National Mall. Once they publicly complain, Obama agrees to remove it from the stimulus, not because he's bowing but because he's allowing republicans to save face. He's allowing them to own the stimulus bill by removing objections. It's not as if those two things are crucial to the stimulus. Behind closed doors they likely discuss the things that aren't up for debate.
It's brilliant salesmanship. It's bipartisanship.