Senate Majority Leader Harry Reid and Senator Richard Durbin (D-Ill.) seem to say "yes":
Please understand that should you decide to ignore the request of the Senate Democratic Caucus and make an appointment we would be forced to exercise our Constitutional authority under Article I, Section 5, to determine whether such a person should be seated.
But Supreme Court precedent suggests "no": The Court held in Powell v. McCormack (1969), that "in judging the qualifications of its members Congress is limited to the standing qualifications prescribed in the Constitution," such as age and citizenship. Now perhaps the Senators are right and the Court was wrong, and perhaps today's Court would overrule Powell. But at least at this point, Powell seems to make clear that under Article I, Section 5 the Senate may determine whether the Senator should be seated solely based on the objective qualifications that the Constitution prescribes, and not based on its judgment whether Gov. Blagojevich ought to be entitled to make the appointment.
(I note that it's conceivable that if there's an allegation that the appointment is the result of a bribe, the situation might be different, but I take it that the Senators' threat isn't limited to such situations.)