In general, I'd tend to tamp down expectations surrounding the potential political fallout from Barack Obama's nomination of another Supreme Court justice later this year, which he'll have to do in the wake of Justice Stevens' retirement. As important as the Supreme Court is, Congressional hearings are still Congressional hearings, and are for the most part inside-the-beltway affairs that won't penetrate into the zeitgeist in a year where most voters have things like the economy on their minds.
With that said, there are two fairly obvious risks here. One is if Obama nominates someone who has a vetting problem, has made an uncouth public statement that makes for a good soundbyte, or has some other skeleton in her (and it most likely will be her) closet. Of course, you'd think the White House would be doing everything in its power to avoid that, but history suggests that no amount of due diligence can completely eliminate these sorts of contingencies (and certainly not contingencies that occur during the hearings themselves).
The risk to Republicans is that they overplay their hand, either by filibustering someone whom the public deems to be reasonable and qualified (which I think they will not do: they can read the polls as well as everyone else) or by basically looking like a bunch of jerks (more risk there: the Senate Republicans are not the most charismatic bunch, although those on the Judiciary Committee are savvier than most). Whatever doubts the public might have had about Clarence Thomas, for instance, the Democrats didn't do themselves any favors during his hearings, which may be one reason that they gained nothing in the Senate (and actually lost seats in the House) even while Bill Clinton was romping to a near-landslide in the electoral vote.
One other dynamic to watch out for: whether the partisan split on Obama has become so entrenched that whomever he nominates will start out with 35 percent disapproval.