Former Rep. Gabrielle Giffords' handpicked successor declined during a Wednesday evening debate to reveal if he intends to vote for President Barack Obama in the November election.

Democrat Ron Barber, who is competing against Republican Jesse Kelly in a June 12 special election for the chance to complete the remainder of Giffords' term, held back from answering Kelly's question about his November voting plans. Barber said instead that he is focusing on his congressional campaign not the presidential race, the Arizona Daily Star reported.

Kelly took this as a opportunity to focus on his opposition to the president's signature health care law, as the Daily Star reported:

Kelly used that demurral as an opportunity to say Barber won't even admit that he supports Obama and "Obamacare," a law that Kelly described as terrible.

"My biggest fear is Mr. Obama's job-killing policies," Kelly said.

The debate -- the second between Barber and Kelly -- comes amid a competitive contest to fill the six-month term in the swing district of southern Arizona following Giffords' resignation from office. Barber, a former staffer in charge of Giffords' Tucson office, has been backed by the former congresswoman and her husband in his race with Kelly, who was narrowly defeated by Giffords in 2010. Barber was shot twice during a January 2011 assassination attempt on Giffords.

Debate during this race has largely centered on Social Security and Medicare, with Barber and the Democratic Congressional Campaign Committee attacking Kelly for his 2009 and 2010 statements calling for the end of the two programs. Kelly's campaign website currently states he does not wish to shutter either program.

Though Barber started his campaign focusing on veterans and border security, he has turned his eye to the two programs. Barber's campaign sent out a press release just after Wednesday's debate, criticizing Kelly on his switch (a retreat from his favoring Social Security privatization) and declaring that he had won the debate.

Following Barber and Kelly's competition over the seat in the Arizona's 8th Congressional District, they'll each run again in an August primary to fill a two-year term in the new 2nd Congressional District; the winners will compete in a general election in November. Kelly faces a GOP primary contest against state Sen. Frank Antenori, businessman Dave Sitton and Gulf War veteran Martha McSally, whom he defeated in the April primary for the special election.

Barber faces a Democratic primary contest with state Rep. Matt Heinz, who dropped his special election plans when Barber entered the race, but has stayed in the regular congressional race even after Barber announced.

UPDATE: 12:19 p.m. -- Barber released a statement Thursday indicating that he is backing Obama, the Daily Beast reported.

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