I think there is a Bradley effect in the polls about Obama, but there are two other factors, comparable to the Bradley effect, that will drag down Clinton and McCain, respectively, in the general election. I suspect the Bradley effect will be quantitatively the least of the three.
For Clinton- Obama has definitely done negative campaigning, but he hasn’t thrown the whole sink at HRC- but the Republicans will. There is a LOT of bad stuff about Clinton which people have forgotten, but which the Republicans will hammer on if she is the nominee. Examples: The attempt to take publicly owned furniture when she left the White House. Lying about Travelgate. The amazing returns on her cattle futures investment. Representing clients in Arkansas in front of regulatory boards appointed by her husband. The pardons when Bill Clinton left the White House- of Marc Rich, of terrorists, and especially HRC’s brothers’ involvement in the pardons.
Clinton even has a "Willie Horton" moment in her past- her minor apparently sympathetic involvement in the Black Panthers murder trial when she was a law student. I don't think she did anything wrong, but wait till Rush Limbaugh gets going on that!
For McCain- most people don’t know how far right he is on domestic issues. His commitment to privatizing social security is going to be pure poison. (George Bush got away with this because Kerry didn’t push the issue- a mistake that neither Clinton nor Obama will repeat.)