Republicans insisted on the delay, saying they needed more time to review Kagan's written answers to questions they posed to her after her confirmation hearings, and to inquire still further into how she would behave as a justice.
CBSNews.com Special Report: Elena Kagan
There's little doubt that the Judiciary panel, where Democrats have a lopsided majority, will approve President Barack Obama's nominee to succeed retiring Justice John Paul Stevens, and that she'll win Senate confirmation within weeks. Democrats have more than enough votes to elevate her, and a handful of Republicans is likely to join them.
But most are expected to vote "no," and of Alabama, the top Republican on the Judiciary Committee, strongly suggested he'll be one of them.
"Fundamentally, the nominee lacks the experience and intellectual rigor that you develop in the full-time practice of law or from serving as a judge," Sessions said of Kagan, who served as solicitor general but has never been a judge or spent substantial time practicing law.
He said Republicans still want to know whether Kagan would recuse herself from cases involving issues that arose while she was serving as the Obama administration's top lawyer, such as challenges to the constitutionality of the president's health care overhaul.
The notion that Kagan didn't weigh in or give advice on the measure in a way that would bar her from ethically ruling on it as a justice, Sessions said, is "difficult if not impossible to believe."
Sen. Patrick Leahy, D-Vt., said he was granting the delay despite his suspicion that everyone on the committee had already decided how they would vote on Kagan. Not surprisingly, he said he plans to support her.
"I believe she will ably fill the seat occupied for decades by Justice Stevens with dignity and honor," Leahy said.
Senators are under pressure, however from the gun lobby and conservative groups to oppose Kagan.
The is asking gun owners to urge senators to oppose Kagan or filibuster her confirmation. The pro-gun rights group said that it planned to begin circulating a Web advertisement this week comparing Kagan's answers on gun issues at her confirmation hearings with those of Obama's first high court nominee, Justice Sonia Sotomayor, who they contend misled senators last year about her support for the right to bear arms.
If confirmed, Kagan, 50, would become the fourth woman on the court, as well as the third sitting female justice.