After the hearings, the full Senate will consider Kagan's confirmation, and even though Democrats fall one vote short of the 60 needed to prevent a Republican filibuster, most experts believe the chances of that are slim.
But Senate Majority Leader Mitch McConnell of Kentucky today refused to rule it out. "It's way too early to be making a decision about the issue of whether there should be a 60-vote threshold on the nominee," he said on ABC's "Top Line."
Kagan was confirmed by the Senate as solicitor general last year with the support of seven Republicans, including two conservatives on the Judiciary Committee: Sens. Jon Kyl and Orrin Hatch.
Democrats will likely make the case in the weeks ahead that if she's good enough to represent the United States before the Supreme Court, she's good enough to be on the court.
Still, the overwhelming majority of Republicans voted "no" on Kagan for solicitor general and some are now expressing skepticism about her lack of judicial experience and controversial views, including her decision as dean of Harvard Law School to block military recruiters from campus because of the services' ban on openly gay and lesbian members.
"She is a surprising choice from a president who has emphasized the importance of understanding 'how the world works and how ordinary people live,'" said GOP Sen. John Cornyn of Texas. "Ms. Kagan has spent her entire professional career in Harvard Square, Hyde Park, and the DC Beltway. These are not places where one learns 'how ordinary people live.'"
McConnell also questioned Kagan's lack of judicial experience. "She's the least qualified [nominee] in terms of judicial experience in 38 years," he said. "Some would argue that maybe we need to have people who don't have judicial experience. I saw a survey indicating about 70 percent of the American people think judicial experience is a good idea for somebody who's going to be on the Supreme Court."
Utah's Hatch, one of the seven Republicans who supported Kagan for solicitor general, cautioned that his vote then does not necessarily mean his support now but said he's keeping an open mind.
"My conclusion will be based on evidence, not blind faith," Hatch said. "Her previous confirmation, and my support for her in that position, do not by themselves establish her qualifications for the Supreme Court or my obligation to support her."
Arizona's Kyl, who also supported Kagan for her current post, agreed. "A temporary political appointment is far different than a lifetime appointment to the Supreme Court," he said.
Some key Republicans on the Senate Judiciary Committee offered more upbeat first assessments of the nominee today, though careful to reserve endorsement until a more thorough review.
Sen. Lindsay Graham of South Carolina said he is "generally pleased" with the job Kagan has done as solicitor general, "particularly regarding legal issues related to the war on terror."
Sen. Susan Collins of Maine praised Kagan's "impressive resume of dedicated public service," while fellow Mainer Sen. Olympia Snowe embraced her "strong intellectual credentials."
Kagan supporters say they expect at least some Republicans to support her confirmation, and any criticism leveled by those who don't will not pose a real threat to her confirmation.