With due respect to congressional Republicans who want to hold President Obama to account for supposedly exceeding his executive authority, and to congressional Democrats who want to hold House Republicans to account for failing to live up to their legislative responsibilities, members of both parties should be focusing now on the question of how to hold the Central Intelligence Agency to account.

CIA officials on Thursday acknowledged that agency operatives spied on computers that were being used by Senate Select Committee on Intelligence staffers who were using to prepare report on an investigation of “enhanced interrogation” techniques and related detention issues. An inquiry by CIA Inspector General David Buckley determined that five CIA employees, two lawyers and three information technology specialists obtained access to what was supposed to be a secure network for the Senate staffers.

The CIA says agency employees “acted in a manner inconsistent with the common understanding” of how the agency and the Senate are supposed to communicate.

The translation from Colorado Senator Mark Udall adds clarity: “The CIA unconstitutionally spied on Congress by hacking into Senate Intelligence Committee computers.”

CIA director John Brennan has apologized to Intelligence Committee chair Dianne Feinstein, D-California, and the ranking Republican on the committee, Georgia Senator Saxby Chambliss.

But if Congress is to maintain meaningful oversight over the federal intelligence agencies, the need for a meaningful response to what Senator Patrick Leahy describes as “a very dark chapter in our nation’s history” cannot be lost amid the usual flurry of internal inquiries, official apologies and “expressions of concern.” As Senator Angus King, an independent from Maine, says, “We’re the only people watching these organizations, and if we can’t rely on the information that we’re given as being accurate, then it makes a mockery of the entire oversight function.”

King is right. But what, then, is the appropriate response?

Udall argues that Brennan should resign. “This grave misconduct not only is illegal, but it violates the U.S. Constitution’s requirement of separation of powers,” says the Colorado Democrat. “These offenses, along with other errors in judgment by some at the CIA, demonstrate a tremendous failure of leadership, and there must be consequences.”

Holding the head of the agency to account is one element of accountability. But the shuffling of those in leadership positions is only a part of a reassertion of the oversight function outlined in the Constitution. As Senator Ron Wyden, D-Oregon, says, there must be a signal that it is “absolutely unacceptable in a democracy” for an intelligence agency to break into Senate computer files and to try to point fingers of blame at innocent Senate staffers.

Christopher Anders, the senior legislative counsel in the American Civil Liberties Union’s Washington Legislative Office, says the matter should be referred to the Justice Department for investigation.

“It is hard to imagine a greater threat to the Constitution’s system of checks and balances than having the CIA spy on the computers used by the very Senate staff carrying out the Senate’s constitutional duty of oversight over the executive branch. It was made worse by CIA Director John Brennan’s misleading the American people in denying any wrongdoing,” explains Anders. “These latest developments are only the most recent manifestations of a CIA that seems to believe that it is above and beyond the law. An uncontrolled—and seemingly uncontrollable—CIA threatens the very foundations of our Constitution.”

A Justice Department inquiry is appropriate.

Ultimately, however, it becomes vital for the Senate to reassert its own authority.

That’s what happened in the 1970s. As the Senate’s own history recalls, “In 1973 the Senate Watergate committee investigation revealed that the executive branch had used national intelligence agencies to carry out constitutionally questionable domestic security operations. In 1974 investigative journalist Seymour Hersh published an exposé in The New York Times uncovering a CIA domestic spy operation in violation of the agency’s charter that had been ongoing for more than a decade. Former CIA officials and some lawmakers, including Senators William Proxmire and Stuart Symington, called for a congressional inquiry.”

Senate leaders tapped Idaho Democrat Frank Church to lead an investigation that would—after “holding 126 full committee meetings, 40 subcommittee hearings, interviewing some 800 witnesses in public and closed sessions, and combing through 110,000 documents”—produce a 1976 report that concluded, “Intelligence agencies have undermined the constitutional rights of citizens, primarily because checks and balances designed by the framers of the Constitution to assure accountability have not been applied.”

Acting on a Church Committee’s recommendation, the Senate in 1976 approved the establishment of the Senate Select Committee on Intelligence. It’s responsibility was to provide “vigilant legislative oversight over the intelligence activities of the United States to assure that such activities are in conformity with the Constitution and laws of the United States.”

The Intelligence Committee should do just that.

As the senior member of the Senate, Judiciary Committee chairman Leahy says, “Congressional oversight of the executive branch, without fear of interference or intimidation, is fundamental to our Nation’s founding principle of the separation of powers. The CIA’s misconduct threatens the institution of the Senate and its role in ensuring the proper oversight of our government.”