The special election matches Republican Jesse Kelly, who narrowly lost to Giffords in 2010, and Democrat Ron Barber, a former Giffords aide.
Giffords relinquished the seat in January to concentrate on her recovery from a gunshot wound to the head. Giffords and Barber were injured in the January 2011 shooting rampage outside a Tucson grocery store.
Democrats have tried to portray Kelly as a tea partyer who is too far to the right for the swing district. The GOP is trying to make the case that Barber would adamantly back the president's policies.