"I think the president made an outstanding nomination," McConnell told reporters after the meeting.
Not all of Kavanaugh's meet-and-greets are expected to be so chummy. Senate Minority Leader Chuck Schumer, D-N.Y., has already vowed to oppose Kavanaugh's nomination with verve.
Sen. Elizabeth Warren, D-Mass., indicated her opposition in a tweet on Tuesday.
Mark Kende, director of the Drake Constitutional Law Center, said the one-on-one meetings are seen by some experts as a tactic to personalize the process between a nominee and his opponents, which could make it more difficult to vote "no" on the Senate floor.
"It's not rocket science in terms of what the purpose is," Kende said.
But the Democrats' base will likely steel their representatives against any potential changes of heart.
"They're going to be very, very aggressive" in their meetings, said Sara Fagen, a political strategist and CNBC contributor who has known Kavanaugh for years. Kavanaugh is "a very brilliant legal thinker, so I think he'll do great, but anybody in his position is going to have prepare significantly," she added.
With a 51-49 minority in the Senate, and Arizona Republican Sen. John McCain away getting treatment for brain cancer, Democrats not only need a united front to vote against Kavanaugh, but they also need to convince at least one GOP senator to break ranks in order to tank Kavanaugh's nomination. One of the potential swing votes on the Republican side, Sen. Susan Collins, R-Maine, called Kavanaugh's credentials "impressive" and pledged a thorough review before making her decision.
Prior to the nomination of Trump's first Supreme Court pick, Justice Neil Gorsuch, the Senate minority could potentially block nominee by requiring 60 votes to confirm him or her through the filibuster rules.
After blocking President Barack Obama's nominee, Merrick Garland, for nearly a year, Democrats tried to prolong the vote on Gorsuch — prompting Republicans under McConnell to change the Senate rules and eliminate the filibuster, thus requiring only a "simple" 51-vote majority to confirm a nominee.
Once Kavanaugh makes his rounds through the Senate office buildings, he is expected to voluntarily testify before the Senate Judiciary Committee in an open hearing. Much like a presidential debate, nominees to the high court spend significant time preparing for the hearings.
"You're trying to anticipate what kinds of questions people will ask you," Fagen said.
Ultimately, McConnell will be the one to bring a vote on Kavanaugh's nomination to the Senate floor. Fagen said there's no reason why the process of confirming Kavanaugh should take longer than the three-plus months it took to move Gorsuch from nomination to confirmation.