May 16, 2010 -- Sen. Jeff Sessions, the ranking Republican on the Senate Judiciary Committee, told ABC News' "This Week" that Supreme Court nominee Elena Kagan "violated the law" by not allowing military recruiting on the Harvard Law School campus when she was dean there, and added the issue is "no little-bitty matter."

But Senate Judiciary Committee Chairman Patrick Leahy, D-Vt., appearing on "This Week" with Sessions, dismissed the argument as "sound and fury signifying nothing."

The controversy revolves around Kagan's decision to prohibit military recruiting directly on the law school's campus because the military's "Don't Ask Don't Tell" policy prohibiting gays from openly serving in the armed forces violated Harvard Law School's anti-discrimination policy.

When the Supreme Court ruled that a law tying federal funding of schools to military recruiting was constitutional, Kagan allowed on-campus military recruiting to resume so the school wouldn't lose funding.

Asked about the issue by host Jake Tapper, Sessions, R-Ala., said, "This is no little-bitty matter, Jake. She would not let them come to the area that does the recruiting on the campus. They had to meet with some student veterans, and this is not acceptable. It was a big error.

"That went on for a number of years," Sessions said. "It was a national issue. People still remember the debate about it.

"She reversed the policy," Sessions said. "When she became dean, they were allowing the military to come back on campus and had been for a couple of years."

Leahy: 'Sound and Fury Signifying Nothing'

Leahy insisted that the whole affair was much ado about nothing.

"Well, this is like in Shakespeare," he said. "Sound and fury signifying nothing. The recruiters were always on the Harvard campus. She's shown her respect for the veterans there. ... Recruiting went on at Harvard every single day throughout the time she was there."

Sessions strongly disagreed.

"She disallowed them from the normal recruitment process on campus. She went out of her way to do so," he told Tapper. "She was a national leader in that, and she violated the law of the United States at various points in the process."

Other Republican voices have been even sharper.

"She, as Dean of the Harvard Law School, took an effort to block the American military from the Harvard campus all the way to the Supreme Court during a war," former Republican House Speaker Newt Gingrich said Saturday night an NRA convention. "And that is an act so unbecoming of an American that she should be disqualified from the very beginning."

Kagan, currently serving as solicitor general, wrote vividly about her decision regarding military recruiting in 2005 in a letter addressed to the Harvard Law School community.

"I have said before how much I regret making this exception to our antidiscrimination policy. I believe the military's discriminatory employment policy is deeply wrong -- both unwise and unjust. And this wrong tears at the fabric of our own community by denying an opportunity to some of our students that other of our students have," Kagan wrote. "The importance of the military to our society -- and the great service that members of the military provide to all the rest of us -- heightens, rather than excuses, this inequity."

Asking Personal Questions About Kagan: Sessions Says "Be Careful"

Amid some reporting on Kagan's personal life, Tapper asked Sessions how far is too far in that area.

"I think you've got to be careful about that," Sessions said. "I don't believe that is a fundamental judgment call on whether a person can be a good judge or not."

Sessions said legal matters were more important.

"We need to know how able they are to ascertain the real legal issues in a case and deciding it fairly and justly. Will they restrain their personal political views and follow the law faithfully and serve under the Constitution? That's the fundamental test in personal integrity," he said. "Those are questions that go to the heart of whether a person will be an able judge or not."

Upcoming Hearings Will Be a 'Big Deal'

Sessions said Kagan's confirmation hearings will be a "big deal" and that they are particularly important because Kagan "has so little other record," having never served as a judge.

Sessions explained he will be looking to understand how broad her reading of the Constitution is.

"I think we'd like to know, in a real honest sense, whether her philosophy of law is so broad in her interpretation of the Constitution that you are not faithful to the Constitution and laws," Sessions told Tapper. "In other words, a judge under their oath says you serve under the Constitution, not above it. So we want to know whether she faithfully will follow it even if she doesn't like it.

"I think we'll be looking at her testimony, because she has so little other record," Sessions added. "It's going to be a big deal. It's so important how she testifies."

'Real Questions' About Kagan

Later, on the This Week roundtable, Salon.com blogger Glenn Greenwald and former Obama White House Counsel Gregory Craig clashed about Kagan's experience.

"There are real questions about Elena Kagan," Greenwald said. "Look at the great legal issues that have confronted the court: Roe v. Wade ... gay rights, affirmative action, the president's authority in the war on terror," he said.

"Can you point to anything that she has said or written in the past that would let Americans know what she believes about those issues?" he asked Craig.

"What you're arguing for here is a judge and [that] only judges should be on the Supreme Court," Craig said. "She's not a judge, so she doesn't have the 17 years of writing opinions that Sonia Sotomayor does."

"But lots of law professors have written numerous things about those questions. Has she?" Greenwald interrupted.

"She's written five or six law review articles. She taught classes," Craig replied.

"So what has she said that would enable people to know about those great issues that have confronted the country and the court," Greenwald asked. "Anything?"

"Yes!" Craig replied.

"What is it? What are those things?" Greenwald demanded.

"Every day Elena Kagan has taught students, administered law professors," Craig said.

"What has she said about those issues?" Greenwald asked again.

"Well," Craig said, "she'll answer questions about that when she's asked."