A vote on the nomination to replace John Paul Stevens, who retired at the end of the last session of the court, was expected Thursday before the Senate heads into its summer recess.
Sen. Jeff Sessions, the top Republican on the Senate Judiciary Committee, warned Kagan would be an activist judge, the Chicago Tribune reported.
"This is not a judge committed to restraint," Sessions, R-Ala., said.
"She possesses a judicial philosophy that does not properly value discipline, restraint and rigorous intellectual honesty," Sessions said in announcing he would vote against confirmation.
Senate Judiciary Committee Chairman Patrick Leahy, D-Vt., defended Kagan, who is currently U.S. solicitor general, as impartial, modest and committed to principle and the law.
"I believe the American people have a sense of her impressive knowledge of the law, her good humor and her judicial philosophy," Leahy said.
Kagan, 50, coasted through the nomination process, The Washington Post noted. Her confirmation would make her the fourth female Supreme Court justice and the third on the current court.
A CNN poll taken in July indicated 54 percent of those queried favored Kagan's confirmation.
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