Oil spill clogging Washington's biggest mouths By: Nikki Schwab and Tara Palmeri Washington Examiner 06/08/10 9:00 PM EDT CNN contributor Alex Castellanos (Photo by Darren McCollester/Getty Images) Since BP bought up some of Washington’s biggest pundits to clean up their image, things are getting sticky. Television bookers are strapped for guests, we hear, and conflicts of interest have cropped up. Take John Feehery. He frequently appears on CNN and MSNBC, but has been working on BP’s account for two weeks with the Brunswick Group. When he appeared on MSNBC’s “The Ed [Schultz] Show” on June 1, the BP story was...