Republican critics laid down a series of markers, though, making clear they will question the 50-year-old solicitor general about her lack of judicial experience, her decision as dean of the Harvard Law School to ban military recruiters from campus, and her ability to rule objectively on cases involving the Obama administration.
Americans "do not want someone to be a rubber stamp for any administration," Senate Republican leader Mitch McConnell said Monday, a few hours after President Barack Obama named Kagan as his choice for the high court. "They instinctively know that a lifetime position on the Supreme Court does not lend itself to on-the-job-training."
Obama introduced Kagan on Tuesday as "my friend" and called her "one of the nation's foremost legal minds."
If confirmed, Kagan would take the place of retiring Justice John Paul Stevens, the leader of the court's liberal bloc, and, on the face of it, would not be expected to alter the ideological balance of a court that often splits 5-4 on the most contentious cases.
"I am confident," Kagan will be confirmed by the end of summer Vice President Joe Biden told CBS' "The Early Show" Tuesday.
"I think they'll be a lot of noise, but this is a mainstream, incredibly qualified woman," Biden said, who added that Kagan will "pass with strong bipartisan support."
Sen. Jeff Sessions, the ranking Republican member of the Judiciary Committee responded to Biden, saying, "This is not a coronation," though declined to say whether or not he thought Kagan would be confirmed by the end of summer.
Assuming she wins Senate confirmation, Kagan would become the third woman on the nine-member court and only the fourth ever. She would be the first new justice in 38 years not to have served previously as a judge.
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Obama e-mailed a video to thousands of supporters in which he said the 90-year-old Stevens has helped justices "find common ground on some of the most controversial and contentious issues the court has ever faced." He added Kagan could "ultimately provide that same kind of leadership," suggesting she had the legal acumen and personality necessary to knit together a majority coalition of five justices as Stevens has done.
The president did not identify any of the cases he was referring to. But Stevens has been on the majority side in recent years in divided court decisions that ruled detainees at Guantanamo had a right to go to court to challenge their confinement, struck down Bush-era military commissions to try suspected terrorists, and banned the death penalty for offenders younger than 18.
Other close cases where Stevens either wrote the opinion or assigned it as the senior justice on the prevailing side cheered environmentalists and supporters of abortion rights. One directed the U.S. Environmental Protection Agency to regulate greenhouse gas emissions from cars and trucks. Another struck down a Nebraska state law that banned a type of late-term abortion.
The Supreme Court hears cases that have worked upward through the American appeals court system and are viewed as pivotal to the U.S. Constitution, the basic law that is the foundation for the country's system of government and judicial protections. The court has grown more conservative with the addition of justices nominated by former President George W. Bush.
Obama doesn't face the voters until 2012, but his decision to videotape a message to his supporters underscored the political context inherent in Kagan's selection.
Most Republicans voted last year against Kagan's confirmation to become U.S. solicitor general - essentially the president's lawyer before the Supreme Court. She will continue in that job through the confirmation process.
Her decision at Harvard to bar military recruiters on campus drew criticism from Republican Senator Jeff Sessions, who said at the time of her earlier appointment that she had "placed her own opposition to military policies above the need of our military men and women to receive good legal advice, even from Harvard lawyers."
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Seven Republicans voted to confirm Kagan, who was approved as solicitor general on a 61-31 vote. At least two of them, Senators Jon Kyl of Arizona and Orrin Hatch of Utah, emphasized Monday that they would approach her appointment to a lifetime job differently than a political post.
Her lack of a judicial background means she has no record of rulings as fodder for Republicans, who may instead question her readiness for the high court given her lack of experience on the bench.
For the most part, Republican-aligned outside groups responded mildly to the nomination, and their attitude as her confirmation hearings approach could help shape the party's response.
Obama, in his announcement, said he hoped the Senate would confirm Kagan in time for her to join the court before the opening of the next term in October.
To accomplish that, senators would need to vote before leaving the Capitol at the end of August for their Labor Day vacation, a timetable that Sessions, the leading Republican on the Judiciary Committee, said "should be doable."
McConnell, the Republican Senate leader, sounded less certain about that.
"Fulfilling our duty to advise and consent on a nomination to this office requires a thorough process, not a rush to judgment," he said.
Democrats hold 59 votes in the Senate, more than enough to confirm Kagan, but one shy of the 60 needed to prevent a vote-blocking delay maneuver by Republicans.
But Democrats were already looking ahead to her approval.
"When Solicitor General Kagan is confirmed, the Supreme Court will have three sitting female justices for the first time," said Senato Harry Reid of Nevada, the majority leader. He called that "a historic occurrence that is long overdue."
Democrats went 15 years without a Supreme Court appointment until Obama chose federal appellate judge Sonia Sotomayor last year to succeed retiring Justice David Souter. Sotomayor became the first Hispanic Supreme Court justice.
Kagan's background, including time as a lawyer and a key domestic policy aide in President Bill Clinton's White House, would give the court a different perspective.