I don’t want to understate how seriously wrong it is that the CIA searched Senate computers. Our constitutional order is seriously out of whack when the executive branch acts with that kind of impunity — to its overseers, no less.

But given everything else that’s been going on lately, the single biggest — and arguably most constructive — thing to focus on is how outrageously CIA Director John Brennan lied to everyone about it.

“As far as the allegations of the CIA hacking into Senate computers, nothing could be further from the truth,” Brennan told NBC’s Andrea Mitchell in March. “We wouldn’t do that. I mean, that’s just beyond the, you know, the scope of reason in terms of what we do.”

Earlier, he had castigated “some members of the Senate” for making “spurious allegations about CIA actions that are wholly unsupported by the facts.” He called for an end to “outbursts that do a disservice to the important relationship that needs to be maintained between intelligence officials and Congressional overseers.”

And what compelled Senate intelligence committee chairwoman Dianne Feinstein to make a dramatic floor speech in the first place, bringing everything out in the open, was that Brennan had responded to her initial concerns not by acknowledging the CIA’s misconduct — but by firing back with an allegation of criminal activity by her own staff.

Not coincidentally, the document the CIA was hunting for, that Senate staffers were accused of purloining, and that Brennan was now lying about, was a big deal precisely because it exposed more lies.

Known as the Panetta Review (evidently prepared for Leon Panetta, who served as CIA director from 2009 to 2011), it became relevant last year, when the CIA started pushing back against many of the scathing conclusions in the several-thousand page “Torture Report” the Senate staffers had finished up in December 2012.

Even as the CIA was officially rebutting key parts of the committee’s report, the staffers realized they had an internal CIA review that corroborated them. In other words, it was proof that the CIA was now lying.

So what’s in the Torture Report? Well, I can’t quote from it, because the intelligence community and the White House have done such a good job of delaying its public release (although a redacted version is widely rumored to be coming soon).

But by all accounts, the report not only discloses abuse that was more brutal, systematic and widespread than generally recognized, but also chronicles how the people most intimately involved in the torture regime lied to others inside the CIA, lied to Justice Department lawyers, and lied to the public; how they lied about what they were doing, they lied to make it sound like it accomplished something, and afterwards, they lied some more.

Brennan reportedly told Feinstein and intelligence committee vice chairman Saxby Chambliss on Tuesday that he was sorry. But it’s hardly the first time he’s been caught in the act. There was, for instance, that time in June 2011, when he was President Obama’s counter-terrorism advisor, that he asserted that over the previous year there had not been a single collateral death from drone strikes. (He later amended that to say there was no “credible evidence” of such deaths.)

But there was indeed ample and credible evidence. (Just as one example, a March 2011 CIA drone attack in Pakistan killed some 50 people, including tribal elders who were gathered for a tribal conclave.)

Brennan’s erstwhile boss, Director of National Intelligence James Clapper, famously lied when he assured the Senate intelligence committee that the government wasn’t collecting data on Americans in bulk when, as it turns out, it was.

Lying, of course, has always been a problem in Washington. But especially after the 9/11 terror attacks, the Bush-Cheney regime took lying to new post-Nixon heights. Maybe even pre-Nixon.

When I sat down to write my last “White House Watch” column for the Washington Post, what struck me most about the Bush years were the lies. The most consequential, of course, were the lies about the war. The most telling were the lies to cover up the lies about the war. And the most grotesque were the lies about torture.

The other thing is that there were no consequences. No one got in trouble for lying. The only semi-casualty was Scooter Libby, briefly convicted of lying while obstructing the investigation into vice president Cheney’s lies.

Figuring out how to right the constitutional imbalance between the branches of government, as exposed by this CIA assault on Congress, is very complicated.

But doing something about lying isn’t. You need to hold people accountable for it.

History will assuredly record that President Obama lied about a number of things, particularly as he carried water for the intelligence community and the military. But he’s no Cheney.

So if you’re the president, you fire everyone who lies. Starting with John Brennan.