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“It’s not a registration. It’s not a registration … but if you’ve lied about it, then that is going to be retained,” he said.

But even with accusations flying and passions on the issue running high after Newtown, the Chicago race may not be the best one to test Mr. Biden’s prediction.

According to Brian Gaines, a political-science professor at the University of Illinois, there are several oddities particular to the race — and he advises against reading too much into a victory by Ms. Kelly.

For example, state Sen. Donne Trotter was arrested for bringing a gun into Chicago’s O’Hare International Airport in December and subsequently dropped out of the race. Ms. Hutchinson’s name also will still appear on the ballot despite her dropping out.

Further, gun control was an issue for Illinois Democrats even before Newtown. On Dec. 11, a three-judge federal panel said the state’s ban on carrying concealed weapons in public was unconstitutional and gave the Illinois General Assembly 180 days to craft some kind of concealed-carry law. On Friday, the full court, minus one judge, denied the state’s petition for a hearing before the entire court.