Republicans are unlikely to look to filibuster Supreme Court nominee Elena Kagan, a senior member of the Senate Judiciary Committee said Monday.

Sen. Orrin Hatch (Utah), the second-ranking Republican on the committee who has at times served as its chairman, downplayed the likelihood of Republicans looking to block Kagan's nomination as the Judiciary panel begins hearings on her this morning.

"I don't think anyone's going to do that," Hatch said during an appearance on MSNBC when asked if a filibuster was in order. "After all, there's 59 Democrats, and I suspect there'll be a few Republicans who will vote for her regardless."

While Hatch had miscounted — he didn't take into account the death of Sen. Robert Byrd (D-W.Va.) early Monday morning — Democrats still remain firmly in control of the Senate with 58 seats. West Virginia Gov. Joe Manchin III, a Democrat, could also appoint an interim senator in time to vote on Kagan's nomination before the whole floor.

While Republicans have expressed reservations so far about filibustering Kagan, they've ramped up their rhetoric in recent weeks against President Barack Obama's choice to replace the retiring Justice John Paul Stevens.

Senate Judiciary Committee Chairman Patrick Leahy (D-Vt.) also predicted confirmation for Kagan on Monday morning.

"She will be confirmed," he said on "Good Morning America" on ABC. "How many votes, I don't know."

Sen. Jeff Sessions (R-Ala.), the ranking member who has in part led the effort to press the case against Kagan, said he was hopeful a filibuster wouldn't be necessary, though he's refused to rule one out.

"I hope we don't have a filibuster," he said alongside Leahy on GMA. "I hope this is a nominee who can move on through."

And while other GOP senators have expressed reservations about Kagan's ability to be an impartial justice, Sen. John Cornyn (R-Texas), himself a former state supreme court justice, said he hadn't concluded that she would be an impartial jurist.

"I think I was and I think she could," Cornyn said of Kagan's ability to be impartial on NBC's "Today" show. "But I think we need to ask her about that."