"You raised your right hand here today and said you would solemnly swear to tell the truth, the whole truth and nothing but the truth", Democratic Senator Martin Heinrich said.
In short, executive privilege is essentially a way for presidents, and members of their administration, to refuse to answer questions. "You're impeding this investigation".
He has been under renewed scrutiny since his role came up several times during testimony before the Intelligence Committee last week by James Comey, whom President Donald Trump fired as Federal Bureau of Investigation director.
"As NPR's Carrie Johnson recently reported on All Things Considered: "[Sources] are telling me Trump has been very angry with Jeff Sessions for recusing himself in the Russian Federation investigation to begin with, lots of profane conversations and yelling. Sessions previously offered to resign because of tensions with Trump over his recusal decision.
Reed said he also wants to know if Sessions had more meetings with Russian officials as a Trump campaign adviser than have been disclosed.
"I am not stonewalling", Sessions replied.
This polarization goes much deeper than just the issue of Russian interference. In a speech about violent crime in Richmond, Virginia, this past March, Sessions called cannabis use a "life-wrecking dependency" and said that it will "destroy your life".
Executive privilege is not explicitly mentioned in the United States Constitution, but presidents have argued it's implied in the constitutionally mandated "separation of powers", according to NPR. Asked if Sessions was of interest to the European embassy because of his role on the Senate Armed Services Committee, the diplomatic source said, "We meet with people from the Hill as often as possible and of course it was well known that Sessions was close to the Trump campaign, he even had a formal role". Comey asked during his testimony last week.
"I do not" Sessions said when asked whether he knows whether the president records his conversations.
Tuesday's hearing may also throw new light on the awkward state of the relationship between Trump and Sessions.
House Speaker Paul Ryan, a Republican, told reporters on Tuesday he had heard only rumors about Mueller, but said, "The best advice would be to let Robert Mueller do his job".
While answering questions about why he didn't alert other officials about Trump's request that he end his investigation of former national security adviser Michael Flynn, Comey said that FBI officials long expected Sessions to recuse himself from overseeing the Russian Federation probe.
He also has vented frustration to aides on Sessions' decision to recuse himself from the Russian Federation investigation, a decision that led to Rosenstein's appointment of a special counsel, Robert S. Mueller III, a former FBI director. He said he would agree to dismiss Mueller only if there were a legitimate basis to do so.
"Senator, I'm not going to follow any orders unless I believe those are lawful and appropriate orders", Rosenstein answered. That came after Comey's public testimony, in which he said the FBI was "aware of facts that I can't discuss in an open setting that would make [Sessions'] continued engagement in a Russia-related investigation problematic".
Burr also noted that the committee has spoken to "more than 35 individuals to date" as part of its Russian Federation probe. Sessions said he did not mislead Congress because the encounters were part of his job as a USA senator, not as a Trump campaign representative.
Trump, his supporters, and right-wing media such as Fox News and Breitbart, on the other hand, declared Comey weak.