The state's senior senator says four Republican senators already support the Democrats but six are needed.
Senate Majority Leader Bill Frist has given Democrats an ultimatum to allow an up or down vote on Bush's designees or prepare for an end to filibusters on judicial nominees.
Democrats have refused to comply.
Durbin says the filibuster ensures all senators have an equal chance to argue their points on the Senate floor. He says changing the rules of the Senate now "assaults a fundamental principle of checks and balances."