Harry doesn’t have the authority nor does the RAT caucus. I think Blago has a checkmate here based on the Illinois Statute that gives him the appointment authority in keeping with Amendment 17. Harry is going to have to muster a 2/3 roll call to get this done and expel the pick. IMHO and IANL.
The senate is the final judge as to who may be seated. If there are any irregularities they can refuse to seat.
The House of Representatives did this with an elected member back in the ‘70’s. They just voted not to seat him.
Harry Reid is checkmating Blago, not the other way round. As Majority Leader he’s telling Blago not to bother since the Federal Constitution trumps State Law in this area.