The answer is easy and ironic. They can do it by taking a page out of the Clinton handbook and painting it as petty politics on the part of the opposition (the Dems, the liberals). They can only pull this off, though, if the other side plays into it — which, with Lieberman’s self-righteous streak, and the unrestrained rhetoric from liberal pundits, they are doing magnficently.
Clinton got out from under most of Whitewater and Interngate by recasting the debate as Evil Ken Starr against a beleagered, admittedly fallible, but basically decent President Bill. If Joe Lieberman isn’t careful, Bush will be able to do much the same, with the Senator as the Simon LeGree figure.
By focusing on the overblown rhetoric of the accusers, defenders of the President can discredit any substantive allegations that come up — if any really do.
Spinsanity has an excellent article on this. It should be required reading, for both sides, like most of that site’s work.