The branch of government that should be the least consumed with party labels is the judiciary. Once appointed to their lifetime tenured appointments, federal judges should hold themselves above politics. I recognize that judges take office with well-established ideological orientations that will influence their decisions, but judges, unlike say, members of Congress, cannot be directly influenced by party politics. In addition, federal judges are supposed to stay out of electoral politics while in office. And most importantly, judges are bound to decide cases according to the law, not according to their political preferences. (Again recognizing of course that the higher the judge's level, the more opportunity there is for legal decisions to be influenced by philosophical and political considerations. The statutory and constitutional questions accepted by the Supreme Court tend to leave a lot of room for interpretation.)
On the other hand, a good argument can be made that what is really needed on the Court at this time is a fiercely liberal voice, in the tradition of a Brennan or Marshall or Douglas, something the Court has not had for some time. Ideally, the Court probably should contain at least one Justice as far to the left as respectable legal opinion allows, to counter-balance the strong voices on the right that we already have, and to keep all of the Justices intellectually honest by forcing them to consider arguments on both the left and right ends of the spectrum. Since Senate Republicans have already signaled that they might attempt to filibuster whomever the President appoints, now might be a good time to challenge the Senate to consider a powerful liberal voice, reserving a more moderate candidate for a potential third appointment. Since the Senate will likely respond to his appointment in a partisan manner, and the Court will probably take on a more partisan appearance no matter who is appointed, the President should have a great deal of freedom to appoint the candidate he feels would be best for the Court in the long run.
(retiring Justice John Paul Stevens)