"The answer is yes," Frist said when asked if he would act to change Senate procedures to restrict a Democratic filibuster. "Supreme Court justice nominees deserve an up-or-down vote, and it would be absolutely wrong to deny him that."
In recent weeks, Senate Democrats have questioned whether Alito, a federal appeals court judge, has the proper judicial temperament and ideology to replace retiring Justice Sandra Day O'Connor.
Several Democrats have said that Alito's views on issues such as voting rights and abortion could provoke a filibuster unless he allays their concerns about his commitment to civil rights. Alito's confirmation hearings begin Jan. 9 in the Senate Judiciary Committee.
Frist, R-Tenn., said Alito is qualified for the high court, noting that Alito was confirmed by the Senate for the 3rd U.S. Circuit Court of Appeals.
"Sam Alito, who has a modest judicial temperament ... is someone who deserves advice and consent by the Senate," Frist told "FOX News Sunday."
The filibuster is a parliamentary tactic whereby senators use their right to virtually unlimited debate to block measures, legislation or nominations. It takes 60 votes to stop a filibuster.
Passing a bill or confirming a nominee requires a simple majority -- 51 senators if all 100 senators are present. The vice president can break 50-50 ties.
Under Frist's scenario, the GOP would seek a parliamentary ruling that declares filibusters are not permitted against judicial nominees. That ruling ultimately would go before the full Senate for a vote, with a simple majority required to prevail. Republicans hold 55 seats.
If that plays out, it then would take a majority of senators present to vote to approve a nominee such as Alito.
Such a move carries great risk. Democrats have threatened to retaliate with a fight that could snarl Senate business for months. Also, it could backfire on Republicans if they were to lose majority control of the chamber.