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Sen. Jeff Sessions of Alabama, the ranking Republican on the panel, said he hopes there won’t be a filibuster, but said he’s concerned that Miss Kagan may be “outside the mainstream” of legal thinking.

Mr. Sessions said Republicans have serious questions to resolve about Miss Kagan, including whether she would be too driven by her political views if she were to take a place on the high court bench.

The GOP was set to grill Miss Kagan on controversial issues from guns to abortion to campaign finance, arguing that she’d bring liberal politics and an antimilitary bias to the job of a justice.

“She’ll have to convince me that all of this liberalism that she’s lived with all her life can be put in a proper place and when she gets to be a judge she’ll be left of center but within the mainstream of judging,” Sen. Lindsey Graham, South Carolina Republican, said on “Fox News Sunday.”

For the second summer in a row, a woman chosen by Mr. Obama was appearing for televised hearings in a cavernous room on Capitol Hill, where the questioning by senators is seldom polite but nominees rarely if ever go off-script.

Miss Kagan’s swearing-in would mark the first time three women were on the court at the same time.

The White House and Senate Democrats are painting Miss Kagan, the first woman to be dean of Harvard Law School or to hold the job of solicitor general, as a pioneering figure and brilliant legal mind who can build consensus on the polarized court.

Later this week, they’ll call conservatives, including two who served in the administration of George W. Bush — Harvard Law School professor Jack Goldsmith and former Solicitor General Greg Garre — in a bid to dispel GOP charges that she’s a liberal rubber-stamp for Obama.

The GOP has worked to brand her a liberal extremist who betrayed the nation during wartime, and plans to try to bolster its case by spotlighting Miss Kagan’s dispute with the Pentagon over military recruiting at Harvard and the policy against openly gay soldiers. Its witnesses later this week include three veterans.

While at Harvard, Miss Kagan barred recruiters from the career services office because the military’s policy on homosexuality violated the school’s nondiscrimination rules. She was also strongly critical of the “don’t ask, don’t tell” policy.

The Pentagon said Miss Kagan’s stance made Harvard ineligible for federal funding under a law that required schools to give military recruiters the same access as other employers.

Mr. Obama, while not present at the hearings, will nonetheless be a key theme for Republicans, who regard Miss Kagan’s nomination as a symptom of what they characterize as the president’s attempts to remake the judiciary with judges who are willing to twist the law to achieve their agendas.

“President Obama wants justices who indulge their own policy preferences. There’s every reason to believe that he’s found that with Elena Kagan,” said Ed Whelan of the conservative Ethics and Public Policy Center.

The fact that Republicans lack the votes to defeat Miss Kagan’s nomination “doesn’t make the hearing unimportant,” Mr. Whelan said. “This is an opportunity for Republicans and critics of the administration and of Elena Kagan to make clear to the American people what this administration is doing.”

The White House has carefully choreographed Miss Kagan’s confirmation process, and knows that much of the public is just now learning who she is.

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