The Senate has begun debating the nomination of Priscilla Owen.
In his opening remarks, Senate Majority Leader Bill Frist said the judge deserves an up-or-down vote.
He says the tactics Democrats have used to block a final vote, requiring a judge to get 60 votes and not 50, aren't fair.
Senate Minority Leader Harry Reid warned that Republicans want to "change the Senate forever" by eliminating the use of the filibuster against judges.
The debate will continue for some time. A test vote on the Owen nomination isn't expected until next week.
Should it fail, Frist is planning a vote to ban judicial filibusters, a move dubbed "the nuclear option" because of the impact it would have on the way the Senate does its work.
Even as senators debate on the floor, other lawmakers are said to be working behind the scenes to try to craft an agreement.