I have always said that a Centrist Party, or a group of independent legislators with centrist tendencies, would derive their power from being the swing votes. Anton Scalia does not affect Supreme Court decisions. Important cases are often decided by Anthony Kennedy, since he is capable of joining either the court's liberals or conservatives as a fifth vote.
But now this Slate profile of Elena Kagan suggests that she may play a similar role, by virtue of unique charm. In any event, our governing institutions depend on building bridges, not standing resolutely on different sides of a chasm, as the Republicans and Democrats in Congress are currently doing.