Sessions is the ranking Republican on the Senate Judiciary Committee. Sotomayor's confirmation hearings begin Monday.
"Every judge must be committed every day to not let their personal politics, their ethnic background, their biases, sympathies, influence the nature of their decision-making process," Sessions said. "When you show empathy for one party, Bob, you necessarily show a bias against another group."
He told Schieffer that Sotomayor has "criticized the idea that a woman and a man would reach the same result," something he said is "philosophically incompatible with the American system."
"I am really flabbergasted by the depth and consistency of her philosophical critique of the ideal of impartial justice," he said.
Judiciary Committee Chairman Sen. Patrick Leahy, a Vermont Democrat, said he "totally disagree[s]" with Sessions' assessment and suggested the Alabama Republican is "grasping at straws" and "nitpicking."
"Here's a woman who is a mainstream judge, and she deserves respect as a judge," he said. "She has a track record. And she has shown to be a mainstream judge. You don't have to guess what kind of a judge she's going to be. I've asked her about her speeches, and she said ultimately and completely the law controls. As a judge, she's shown over and over again, ultimately and completely the law controls."
He said Republican opposition "gives the impression that a lot of people were going to oppose anybody, anybody that President Obama came up with."
Schieffer asked Sessions if he would really try to stop Sotomayor's nomination (which is widely thought to be likely to succeed), or if he would simply use it as a so-called "educational moment."
"I hope it is an educational moment because I think we are moving at a crossroads in American jurisprudence," Sessions said. "Are we going to adhere to the classical view of the role of a judge as a neutral arbitrator not out to promote an agenda or an ideology, or are we going to have a restrained judge who follows the law in case after case?"
Leahy said he hopes the hearings do not "turn into a partisan fight."
"Chief Justice Roberts is not somebody I would have recommended as a nominee to President Obama," he said. "But I voted for him when he was nominated by President Bush because I felt Chief Justice of the United States should not be on a party-line vote."
More from Face The Nation (7.12.09):
To watch Senators Leahy and Sessions debate Sotomayor, Cheney and investigations, click on the video player below.
Click on the video player below to watch a roundtable discussion, featuring Kevin Merida of the Washington Post and syndicated columnist Kathleen Parker, about a possible investigation into the Bush administration's use of torture tactics and its concealment of a CIA program from Congressional overseers.