"Vice President Biden directly contradicted the sworn testimony of the State Department in the debate the other night. That led to another round of kind of nuancing by the White House," Gillespie said, adding: "There are inconsistencies here, and I think as Americans we deserve to know what really happened going into this attack."

Gibbs rejected the criticism, calling Republicans who disparage the White House response "wing-tipped cowboys" engaged in "shoot-from-the-hip diplomacy."

The town hall-style debate Tuesday will focus on both domestic and foreign policy issues, making it likely the Libya issue will arise during questioning from the audience of undecided voters.