The Democrat made the announcement on a local political talk show in Tucson. Barber says his family is the main reason he will not be running again for U.S. Congress.
Barber was district director for Rep. Gabrielle Giffords when he and the congresswoman were wounded in a mass shooting at a political event in Tucson in January 2011. Barber won a special election to fill out the remainder of Giffords' term after she stepped down in early 2012.
He defeated retired Air Force pilot Martha McSally in that year's general election to win a full term in Congress. But the 69-year-old lost in a rematch with McSally in November by just 167 votes in a recount that dragged on for weeks.