I have been doing some reading about this lately. (Pat Buchanan wrote an interesting column.) It appears that the Senate is REQUIRED by law to seat Burris. Blago is still the governor of Illinois, and as such has a right, even a duty, to appoint someone to represent Illinois. The Illinois Secretary of State does not have discretion in this case; he is required by law to certify what Blago has already done, and a state court could order him to do so.
True, the U.S. Constitution does give the Senate the right to judge the qualifications of its members, but no one is alleging that Burris does not meet the qualifications.