corporations have the power to exit, by locating headquarters overseas, essentially trading its "US citizenship" for one of a number of more attractive locations. Though I admit, corporations can't do this costlessly.
Why is the threat of exit, in this case, not leading to corporations getting more of what corporations want from politicians?
In fact, the threat of exit does get used and it does work. "If you do X, then this financial market will move to London" was a threat that was often used to talk Washington out of doing X with respect to financial regulation.
However, the threat of exit is often not credible, for various reasons. For one thing, once you relocate your headquarters, your ability to influence U.S. policy diminishes. For example, suppose that AIG or Goldman had moved their headquarters overseas five years ago in order to escape high U.S. corporate tax rates. Would they have received as much government support in the crisis?
Within the U.S., there is some evidence that economic activity has shifted away from business-hostile "blue" states to business-friendly "red" states. To the extent that this is true, it does not seem to have caused politicians in blue states to switch colors.
[UPDATE: Tim Worstall says that it is easier for European companies to relocate within the EU than it is for a U.S. firm to leave to go to the EU. The next question is whether one can see an effect of this greater mobility on policy. That is, does the greater mobility increase the political effectiveness of the threat to exit?]