The governor says a new senator should be chosen by special election.
Burris was appointed by former Gov. Rod Blagojevich, who was later impeached and removed from office.
Burris initially said there was no discussion of him doing Blagojevich any favors in exchange for the appointment. But Burris later acknowledged he did discuss the vacant seat with the governor's friends and allies. He says he was asked to raise money for Blagojevich but couldn't find anyone willing to contribute.
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