No, Barack Obama's former White House Press Secretary Robert Gibbs is not a Jew.
Gibbs was born in Auburn, Alabama on March 29, 1971. He is married to Mary Catherine Gibbs, an attorney. They live in Alexandria, Virginia with their six-year-old son. Gibbs' parents now live in Apex, North Carolina, where his mother Nancy is acquisitions director for the libraries at Duke University.
Of note, Gibbs went on a tirade in 2009 against Sean Hannity, the Fox News host, on his show to prove the vacuity of charges of guilt by association that were being leveled at Barack Obama. To make his point, Gibbs forcefully charged that Hannity was an anti-Semite because he had previously had on an anti-Semitic guest.