Taking us behind the scenes, Paulson shows, day by day, how the U.S. government and Federal Reserve got sucked into a vertiginous game of chicken with Wall Street bankers (link)
Building on the definitions cited by RegDwight, I would explain the sentence as follows.
The bankers' actions put them on a collision course with the government and the Fed.
The potential for disaster was so great that all involved got dizzy thinking about the worst possible results.
Vertiginious comes from vertigo, so it's something that's whirling around, causing dizziness.