Should the congresswoman not be able to finish her term, here's what would go down:
While Giffords' seat could become open through resignation, or in the case of her death, the U.S. Constitution mandates that, in the case of a vacancy in the House, the only way to fill a seat is through an election in the district.
There is no specific provision for the presumed incapacitation of a sitting House member, although a procedure does exist to remove the congresswoman from her seat if she is unable to perform her duties.
The only time this was performed was in 1981, when the House voted to declare Maryland Representative Gladys Spellman's seat vacant four months after she became comatose from a heart attack. She remained in a coma until her death in 1988.
In any circumstance in which Giffords' seat would become vacated, Governor Jan Brewer would be required to call a special election within 72 hours, which would follow the format of an actual election, including party nominations.
The newly elected representative would serve the remainder of Giffords' original term, which would last until 2012.
Giffords defeated Republican newcomer and Iraq war veteran Jesse Kelly by fewer than 4,000 votes in the November election, which may hint toward where that seat would land if it were vacated by the incumbent Giffords.
Until Giffords is gone or back, the congresswoman's staff can help constituents with information about legislation or casework, but nobody can vote in the House on her behalf.