I am going to assume that the Democrat strategy is to nominate someone for the Republicans to criticize, then withdraw that nomination and nominate someone who appears to be less socialist, but who is and who Obama really wanted in the 1st place.
I assume the strategy here is to nominate Kagan and let the Republicans expend all of their rapid opposition on her. Then Obama withdraws her name from nomination, citing that he disires bipartisan cooperation, even though he has the Senate and could install Kagan on the court.
Then he nominates who he really wanted all along, now that the Republicans have shot their wad opposing Kagan. If they oppose nominee #2, the media will brand them as nothing but obstructionist. So the Republicans will ultimately cave in and allow nominee #2 so they don’t look mean.
Meanwhile, Obama gets his 1st choice for SCOTUS with nominee #2. The ace in the hole is to select the right cannon fodder in case the Repulicans cave on nominee #1. So Kagan is someone Obama can live with, but his preferred nominee will come next, after having Kagan withdraw her name for family reasons or some such.