The leaders of the House committee investigating the latest incident of possible Secret Service misconduct fired off an angry letter to the agency's director Sunday, asking that more top officials be permitted to testify at a hearing later this week.

House Oversight Committee chair Rep. Jason Chaffetz, R-Utah, and ranking member Elijah Cummings, D-Md., said that they were "sorely disappointed" that Secret Service Director Frank Clancy said that he would be the only witness to appear at the scheduled hearing Tuesday.

"Your position is not acceptable," the letter said in part, "both because of the public interest in transparency with respect to the agency's ability to protect the President and his family, and because you have not answered our questions adequately to date." The committee had asked for four officials to appear alongside Clancy at the hearing. Clancy did not explain why the other invited officials would not be attending. 

Chaffetz and Cummings said that Clancy had been unable to answer what they called "fundamental questions" about an incident on the evening of March 4, in which two Secret Service agents drove into the scene of a suspicious package investigation near the White House. The agents were allegedly intoxicated when they drove through the area and nudged a construction barrier with their vehicle.

Published reports at the time claimed that a supervisor on duty prevented officers who witnessed the incident from arresting the two agents and performing a sobriety test. 

In an interview with FoxNews.com Friday, Chaffetz also questioned a claim by the Secret Service that key surveillance footage of the March 4 incident had been taped over as a matter of policy. Chaffetz called the claim "highly suspicious" and said he had "a hard time believing that's true." Sunday's letter from Chaffetz and Cummings said that the lack of available video had "further limited the Committee's understanding of the incident."

Lawmakers have been shown two tapes so far – one of which Chaffetz called "clearly useless" - but footage from other fixed positions around the White House grounds may be lost because of the Secret Service's apparent practice of taping over most footage after 72 hours.

Fox News' Chad Pergram contributed to this report.