Sen. Lamar AlexanderLamar AlexanderThis week: Government funding deadline looms Key Republicans ask Trump to keep on NIH director McConnell tees up medical cures bill MORE (R-Tenn.) stressed Saturday that he could exercise a filibuster of President Barack ObamaBarack ObamaMan who plotted to kill Obama sentenced to 30 years Overnight Tech: FCC eyes cybersecurity role | More trouble for spectrum auction | Google seeks 'conservative outreach' director Madonna on Trump win: 'Women hate women' MORE's Supreme Court nominee "if the president picks someone from the fringe or somone who applies their feelings insted of applying the law."
That, the GOP conference chairman said on "Fox News Sunday," could qualify for the "extraordinary case" cited in his Friday statement in which the senator reserved "the prerogative" to cast a no vote or block an up-or-down vote on the nominee.
"I'm not about to start kicking nominees I would reject before the president even makes one," Alexander said.
He did, however, allude to Obama's statement Friday that he would pick a nominee who "like Justice Stevens, knows that in a democracy, powerful interests must not be allowed to drown out the voices of ordinary citizens."
A Supreme Court justice, Alexander said, is "not supposed to be someone you can particularly depend on to be on your side in a controversial case," but should be impartial at all times.
Alexander repeatedly stressed that he had voted for Justice Sonia Sotomayor.
Sen. Joe Lieberman (I-Conn.), when asked whether Obama should pick a moderate nominee to avoid a down-and-dirty confirmation fight, noted that President George W. Bush picked nominees -- Chief Justice John Roberts and Justice Samuel Alito -- that were not "provocatively conservative."
Obama, said Lieberman, should have an eye toward a nomination that would avoid "a knock-down, drag-out battle in an election year," someone who "will not have a record on the court or off that will provoke a filibuster."
"President Obama may nominate someone, in fact, who makes the court slightly less liberal, at least for a while," Lieberman said, noting Stevens' position as the leader of the liberal wing on the court.
Two key Republican senators said Sunday, though, that it is unlikely the GOP
will try to filibuster whomever Obama nominates to
fill retiring Supreme Court Justice John Paul Stevens's seat.
But both Sens. Jeff SessionsJeff SessionsCould bipartisanship rise with Trump government? Top Dem signals likely opposition to Sessions nomination #NeverTrump can love him or hate him, Trump always wins MORE (R-Ala.) and Jon Kyl (R-Ariz.), both members of the Senate Judiciary Committee, said they would not take the tool off the table should Obama nominate someone they view to be outside the mainstream.
Sessions, the committee's ranking member, said on NBC's "Meet the Press" that he would promise a fair hearing and a chance for the nominee to rebut whatever criticisms are made, but he declined to rule out the use of a filibuster.
Sessions pointed to Goodwin Liu, Obama's nominee to the U.S. Court of Appeals for the Ninth Circuit, as someone who is "so activist" that a filibuster would be warranted.
"I just hope that doesn't happen," Sessions said.
Committee Chairman Sen. Pat Leahy (D-Vt.) warned Republicans not to try to block Obama's nominee, calling a filibuster the "lazy person's way out."
Sen. Chuck SchumerCharles SchumerDems press Trump to support ‘Buy America’ provision in water bill Overnight Finance: Trump takes victory lap at Carrier plant | House passes 'too big to fail' revamp | Trump econ team takes shape Anti-Defamation League: Ellison's past remarks about Israel 'disqualifying' MORE, who is also on the committee, said on ABC's "This Week" that Obama in all his appointments has nominated "people in the mainstream," adding that he thinks the "likelihood of a filibuster is tiny."
Kyl, also appearing on "This Week," said that while he would never take a filibuster off the table, he does think it's unlikely.
"President Obama himself attempted to filibuster Justice Alito, who now sits on the Supreme Court," Kyl said. "So if the president isn't going to take it off the table, I'm not going to take it off the table."
While none of the senators would weigh in on the specific names being bandied about that are thought to be on Obama's short list for the vacancy, Schumer did say he would like someone who could perhaps influence Justice Anthony Kennedy.
"I'd like the new nominee to be one of five, not one of four when the votes come up, and somebody who would be quite persuasive in terms of influencing other justices, I guess particularly Justice Kennedy, to his or her point of view," Schumer said. "And that would matter to me more than any particular ideology."
Obama said Friday he will make his decision in the coming weeks so his nominee can be confirmed and seated before the fall term begins in October.
Leahy expressed confidence Sunday that the Senate can meet the president's deadline.
"I think you're going to hear a nomination very soon so we can get this wrapped up this summer," Leahy said.
This story was updated at 11:25 a.m.