Appointment of Obama's replacement

The right of the Governor to appoint the Senator is absolute, under Illinois law...as long as he is Governor. The U.S. Congress has certain Constitutional rights regarding the actual seating and removal of members.

Article I. Section 5
Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members...Each House may determine the Rules of its Proceedings, punish its Members for disorderly Behavior, and, with the Concurrence of two-thirds, expel a Member.

There's a very simple and legal method for preventing the appointment of anyone. It doesn't require any Senate action. Under the Rules of the Senate, a certificate for the appointment must be presented. The Secretary of State must sign it in addition to the governor of the state. The Illinois Secretary of State (Jesse White) can refuse to do it...to block any appointment by Blaggy.