Rep. Ileana Ros-Lehtinen, R-Fla., criticized the "song and dance" she said came from Clinton when House members wanted to question her about Benghazi a few months after the attack. Clinton's testimony before the House Foreign Affairs Committee was delayed when she missed a month of work toward the end of her tenure after suffering a virus, then a fall and a concussion, and then brief hospitalization for a blood clot near her brain.
Benghazi has produced 13 public hearings, the release of 25,000 pages of documents and 50 separate briefings. The select committee won't be the only inquiry, as other GOP-led congressional panels continue their investigations, including a House Oversight probe which just last week took the extraordinary step of subpoenaing a Cabinet member, Secretary of State John Kerry. Kerry hasn't said when he might testify.
Democrats deride the effort as a conservative campaign designed to energize Republican voters in typically low-turnout midterm elections.
Rep. Gerry Connolly, D-Va., accused Republicans of perpetuating "myths and conspiracies" and remaining obsessed with "recycling tired and worn talking points in a cynical attempt to fire up the GOP base in the run-up to an election year."
Earlier this week, the National Republican Congressional Committee sent an email vowing that "no one will get away" from the committee's investigation and asking people for donations.
Rep. Trey Gowdy, R-S.C., the former prosecutor tapped by Boehner to head the panel, has signaled he would re-examine the entirety of the Benghazi attack, including questions Democrats and some senior Republicans consider settled.
Some Democrats dismiss the notion that the public will pay attention.
"I think the American people are not interested in Benghazi," said Sen. Chuck Schumer, D-N.Y. "It appeals to the narrow base of the Republican Party."
Wasserman Schultz's remarks were made in an interview Friday on CNN.
Associated Press writers Bradley Klapper and Alan Fram contributed to this report.