Well you would have to point out which Senate rule prevents judicial appointments from being filibustered. According to Rule XXII, it takes 60 senators to close debate on "any measure, motion, other matter pending before the Senate." It doesn't exclude judicial nominations.
That's exactly the rule that Cheney would declare unconstitutional under the Senate rule that allows him to. That is exactly what the "constitutional" and/or "nuclear" option is. He would declare that rule can't apply to appointments that the constitution declares requires 50% plus 1 to pass.