Officials from the Justice Department and the White House met with senior aides to House Speaker John Boehner and Oversight Committee Chairman Darrell Issa at the White House on Tuesday to try to head off a House vote holding Attorney General Eric Holder in contempt of Congress.

But their offer to show congressional investigators some documents related to the failed "Fast and Furious" gun-trafficking program was rejected.

According to a summary of the offer provided by a senior administration official and a Justice Department official familiar with the discussions, the Justice Department outlined an offer that included giving Congress access to some of the documents generated between Feb. 4, 2011, when the Justice Department initially told Congress there was no inappropriate activity, and Dec. 2, 2011, when it acknowledged the program was "fundamentally flawed."

"We reached out and showed them a representative sample of the documents so they could see firsthand the types of communications in contention," said the administration official, who spoke on the condition of anonymity. President Barack Obama has asserted executive privilege in the dispute.

The Justice Department also offered to conduct a briefing, give Congress documents related to the whistle-blowers, and work with the committee to respond to any questions it had after reviewing the materials. According to a summary of the offer, the Justice Department maintained that this would have given Congress "unprecedented access to deliberative documents."

The administration official said the documents would "dispel any notion of an intent to mislead Congress."

One senior House GOP aide confirmed that the Justice Department made the offer to senior Republican staff, but said it wasn't sufficient. GOP leaders plan to move forward with a House vote to hold Holder in contempt of Congress, which is scheduled for Thursday.

Regarding the offer, White House spokesman Eric Schultz told CNN: "This was a good faith effort to try to reach an accommodation while still protecting the institutional prerogatives of the executive branch, often championed by these same Republicans criticizing us right now. Unfortunately, Republicans have opted for political theater rather than conduct legitimate congressional oversight."

Also Tuesday, the No. 2 Democrat in the House signaled that some Democrats could join with Republicans to hold Holder in contempt, citing pressure from the National Rifle Association.

Republicans on the House Oversight Committee approved a resolution last week holding Holder in contempt for failing to release documents related to the committee's investigation of "Fast and Furious."