WASHINGTON — The latest in a string of baffling missteps by the Secret Service prompted fresh questions Thursday about whether the Obama administration has done enough to root out deep-seated problems plaguing the agency — and President Barack Obama’s decision to put an insider in charge despite his administration’s own review that called for exactly the opposite.

The White House said Obama still has full confidence in recently appointed Director Joseph Clancy, despite a new investigation into two agents accused of driving into White House security barrier after drinking. Obama’s aides described Clancy as the right man to fix problems.

“Nobody has higher standards for the Secret Service than Director Clancy,” said White House spokesman Eric Schultz.

Yet lawmakers charged with overseeing the agency were aghast and wondered how the Secret Service still hasn’t corrected problems involving behavior of its agents. In a rare move, the top Republican and Democrat on the House’s oversight panel joined forces to say that while many of the agency’s top leaders have already been replaced, “this incident begs the question of whether that is enough.”

“Clearly this incident is a major wake-up call,” the Democrat, Rep. Elijah Cummings of Maryland, said later in an interview.

The two senior agents — including Mark Connolly, the No. 2 on Obama’s security detail — had been with other agents drinking at a bar last week when they returned to the White House in a government car, a U.S. official said. The vehicle entered an area already closed off by the Secret Service, who were investigating a suspicious package and had put the White House on lockdown. Officers on the scene saw the agents’ car, traveling slowly, make contact with a barrier, the official said.

A surveillance video captured the entire incident, the official said. Congressional staffers were briefed Thursday on the video’s contents.