First, Posner's line is very similar to Ronald Dworkin's, particularly in that judges must keep their decisions modest and in accord with precedent, but may diverge with good reason. It's not a Hartian view, certainly, which allows judges pretty much unlimited discretion when there "is no law", but no discretion (except in terms of interpretation) when it comes to "settled law".
Second, however, is Posner's claim that judges "have to be seen to be doing law rather than doing politics". I don't quite see the justification for this. Why shouldn't we accept that judges are political actors, particularly in the Supreme Court, and thus evaluate judges as political actors? Indeed, this would open up the (in my view, needed) possibility that judges would not merely be lawyers, but also trained in general critical thought, with particular emphasis on the political.