Marbury v Madison v Cheney

I've got to be way off base here, but what gives Cheney the right to decide whether filibusters against judges are unconstitutional? I thought the Supreme Court decided what was constitutional.

It would seem to me that if Cheney does what he hopes to be able to do, any Democratic Senator could bring a case before the Supreme Court claiming they were injured by his decision, and that would lay it in the lap of the Supreme Court, where it belongs.

I'm obviously not a lawyer. I know the Senate has the right to make its own rules, but don't those rules have to be constitutional, and isn't the Supreme Court the place to decide it?

Somebody set me straight on this, please.