It was no surprise that Sessions, the ranking GOP member of the senate Judiciary Committee, echoed Republican sentiments by saying Kagan "has the least experience of any nominee at least in the last 50 years."
"So I think that raises questions. I've been using the phrase, you know, 'This is a confirmation, not a coronation,'" he said.
It was also no surprise that Leahy, the committee's chairman, countered the criticism by saying: "I think you're going to see a brilliant woman, a brilliant legal mind, and you're going to see somebody who is going to be the 112th justice of the U.S. Supreme Court."
Leahy even quipped that the party lines have already been drawn before the hearings commence Monday.
"It's reached the point that if [Obama] had nominated Moses the law giver, some would have said we can't have him because among other things he hasn't produced a birth certificate," he said.
Sessions told CBS News chief Washington correspondent Bob Schieffer that a filibuster of Kagan is not off the table.
"I think the first thing we need to decide is, is she committed to the rule of law even if she may not like the law?" Sessions said. "Will she as a judge subordinate herself to the Constitution and keep her political views at bay? And then secondly, if things come out to indicate she's so far outside the mainstream, it's conceivable a filibuster might occur."
When asked if he believed Mr. Obama's pick was even qualified for the Supreme Court, Sessions responded sharply: "I think her nomination has real problems that need to be examined. I believe she's entitled to a fair hearing and a chance to respond, but this nominee has a very thin record legally - never tried a case, never argued before a jury, only had her first appearance in the appellate courts a year ago. She just is not the kind of nominee you would normally expect to have."
CBS News chief legal correspondent Jan Crawford raised a point to both senators that the battle over the nominee's confirmation hearings falls largely along rigid party lines - and pointed to earlier conflicts over High Court nominees.
Crawford asked Leahy about the confirmation hearings for President Bush's Supreme Court nominee (now Justice) Samuel Alito. Crawford said that despite support for Alito from liberals (similar to support Kagan has received from conservatives) and the highest rating from the American Bar Association, Leahy voted against Alito's nomination, and that he and then-Senators Barack Obama and Joe Biden thought that he should be filibustered.
Leahy responded, "I voted for John Roberts - very Conservative. Had been in the Reagan and Bush administrations. But I felt that he gave us direct and honest answers.
"I felt that Justice Alito did not," Leahy said. "That is why I voted against him."
Leahy also added, "Keep in mind I voted for hundreds, even thousands of judges nominated by Republicans; President Reagan, both President Bushes, President Ford, who were not the people I would have nominated had I been president. But I felt after going through the hearing that they were people that I could trust to uphold the law. I didn't feel that way [about Justice Alito]. I hoped Justice Alito would prove me wrong."
Crawford turned the focus to Sessions and mentioned his position seven years ago on filibustering - a stark difference from his position now as the Kagan confirmation hearings approach.
"In 2003 when the Democrats were filibustering, you told [PBS'] Jim Lehrer it was a very, very grim thing. You said it would weaken the hand of the president and a constitutional alteration of power," Crawford said.
Sessions responded to why his position with President Obama's latest nominee is different: "We just have to live with the world we're in, Jan.
"The filibuster [in 2003] was ongoing by the Democrats on quite a number of Bush judges for the first time in history. The compromise that was reached with the 'Gang of 14' was that you should not filibuster except in extraordinary circumstances. I've never filibustered a Supreme Court Justice. I hope I don't have to. We didn't with [Justice Sonia] Sotomayor."
For all the debate over President Obama's second Supreme Court nominee in as many years, Leahy told Schieffer that people's minds won't be swayed until they hear from Kagan herself.
According to Leahy, "Right now we've debated almost in a vacuum. Let's hear from her. At the end of the week people's views may be entirely different. Let her answer these questions."