Elena Kagan sought to position herself Monday as someone who would be a neutral arbiter if confirmed as a justice on the U.S. Supreme Court, defying hopes from the political left and right that she would outline a clear judicial philosophy during her confirmation hearing.

Kagan, in her opening statement, echoed comments from previous nominees in declaring that she would put ideology aside as a judge. “I’ve learned that we make progress by listening to each other, across every apparent political or ideological divide,” she told the Senate Judiciary Committee. “I’ve learned that we come closest to getting things right when we approach every person and every issue with an open mind.”

Her comments did not stop senators from trying to frame Kagan’s nomination on their own terms. They said the Supreme Court is embroiled in high-stakes battles in which the decisions are polarized, and they urged Kagan to say where she would come out.

Senators will begin questioning Kagan on Tuesday, but she warned them not to expect any promises about her future positions. “I will make no pledges this week,” she said, other than to abide by lessons about working hard and listening to her colleagues.

Most Republican members of the committee attacked Kagan’s qualifications, noting that she has never been a judge, and they said they were concerned about her political and policy work in the Clinton White House. “Not only is Ms. Kagan’s background unusual for a Supreme Court nominee, it is not clear how it demonstrates that she has, in the president’s words, ‘a keen understanding of how the law affects the daily lives of the American people,’” said Sen. Jon Kyl (R-Ariz.).

Democrats rushed to Kagan’s defense, pointing out that one-third of Supreme Court justices in U.S. history never previously served as judges. Kagan broke barriers, they said, as the first female solicitor general and the first female dean of Harvard Law School. “You’ve had a lot of practical experience reaching out to people who hold very different beliefs, and that’s increasingly important on a very divided Supreme Court,” said Sen. Amy Klobuchar (D-Minn.), adding that most prior solicitors general since 1985 are supporting Kagan.

The Kagan hearings began on a day that saw the death of Sen. Robert Byrd (D-W.Va.), the longest-serving senator in U.S. history. Senator after senator paid tribute to Byrd in his or her remarks, with some also paying respect to Martin Ginsburg, the husband of Justice Ruth Bader Ginsburg, who died over the weekend.

On a less somber note, it was also the last day on the bench for Justice John Paul Stevens. Kagan saluted him in her opening statement, as well as former Justice Sandra Day O’Connor and Justice Ruth Bader Ginsburg for their work in creating “boundless possibilities for women in the law.”

Before the hearing began, an administration official said that Kagan stopped at the White House for a meeting with President Barack Obama. Obama, who was out of town this weekend meeting with other world leaders in Toronto, wanted to offer encouragement and wish her good luck, the official said.

An array of administration officials came out to support Kagan. Sitting just behind her was Philip Schiliro, who is President Barack Obama’s chief adviser for legislative affairs; Susan Davies, a deputy White House counsel who leads the administration’s process for selecting federal judges; and Chris Kang, one of Schiliro’s deputies. Also sitting in the front row was Acting Solicitor General Neal Katyal, who has served as Kagan’s chief deputy, and White House Staff Secretary Lisa Brown, a former executive director of the liberal American Constitution Society.

In opening statements at the hearing, GOP senators invoked Kagan’s close connection to the White House in debating whether she would be a “rubber stamp” for Obama’s policies.

But at least one Republican left open the possibility of support. Sen. Lindsey Graham (R-S.C.) was the only Republican on the Judiciary Committee to support Justice Sonia Sotomayor a year ago. On Monday, he continued to drop hints that he might be willing to vote for Kagan, too.

Graham told Kagan at her confirmation hearing that “there’s no doubt in my mind that you’re a liberal person.” But, he added, “That applies to most of the people on the other side. I respect them and I respect you.”

He said that “elections have consequences” — a phrase that Republicans used often during George W. Bush’s administration to emphasize the president’s power to nominate.

“What did I expect from President Obama? Just about what I’m getting,” Graham said. “A lot of people are surprised. Well, you shouldn’t have been, if you were listening.”

David Ingram can be contacted at dingram@alm.com.