"He went in and just started firing and then he ran," said Hernandez, prompting the operator's exclamation.
Giffords, a representative for Arizona's 8th District who just won reelection to a third term, has been the target of conservative political opponents in recent months.
Last March, Giffords' office was vandalized just after she voted in favor of the health care reform law. The intruders destroyed a glass door and a window at her Tucson Congressional offices.
At the time, Giffords' press secretary C.J. Karamargin said the office had received many phone calls with "nasty and rude and hateful comments" from opponents of the health care bill.
Recently Giffords, who supports gun rights, has received angry letters from anonymous sources, ranting about the supposed national gun registry and border control.
One letter received on Dec. 15 addressed to "giffords, obama, mccain and sen. Jon kyl" got personal on the topic of U.S. Border Patrol Agent Brian A. Terry, who was killed in a late night shootout at the U.S.-Mexican border.
"Brian a Terry's blood is on your hands! How many more legal residents of the USA have to die before the border is CLOSED??? Obama I call you out! CLOSE THE DAMN BORDER NOW! Quit pandering to illegals!," the letter read.
Giffords has a reputation as a political rebel. Though though she supported her party's effort to pass a landmark health reform law, she voted with the Democratic Party only about 40 percent of the time, according to Congressional Quarterly,.
She was also one of a handful of Democrats who did not vote for Nancy Pelosi for speaker of the house, during the recent Democratic leadership elections after Democrats lost their majority in the House last November.
ABC News' Rich Esposito, Pierre Thomas, Jack Date, Jason Ryan, Gina Sunseri, Ross Eichenholz, Toni Wilson, Desiree Adib, Kevin Dolka, Dean Schabner, Sherisse Pham, Amy Walter, Leezel Tanglao, Devin Dwyer, Erin Keohane and the Associated Press contributed to this report.