Waxman said he'd work with Burgess to write a letter requesting the information instead of relying on the House to pass a resolution launching an official inquiry.
"A resolution of inquiry is a serious oversight tool and it should not be used unless other avenues to obtain information have been undertaken and exhausted," Waxman said.
Burgess' resolution would have encompassed notes of communication between the president and his chief of staff and other top advisers, presidential e-mails, and other high-level deliberations.
"There has been no showing -- or even an allegation -- of wrongdoing that would justify this kind of request," Waxman said.
Although his resolution essentially failed, Burgess said he was pleased with the outcome of the markup.
Waxman's agreement to work with him "somewhat surprised" him, he said, although Waxman has a long record of a "commitment to being open and above-board."
Indeed, Waxman has been an advocate of government transparency and has launched numerous inquiries, including an investigation of the FDA's handling of rosiglitazone (Avandia) after a meta-analysis linked the drug to increased cardiovascular risk.
During the markup, Republicans accused the administration of breaking its promise to increase transparency. Democrats, meanwhile, defended the White House for being significantly more transparent than the Bush administration.
The Bush administration came under fire for keeping a tight lid on negotiations that led to the formation of its energy policy. For years Reps. Waxman and John Dingell (D-Mich.) tried to get the Bush administration to disclose information from the closed-door meetings.
"The White House consistently rebuffed these requests," Waxman said.