I read on another posting where someone stated that Congress has the power to remove any federal official, from the highest ranking Executive or Justice of a Court to the lowliest appointed bureaucrat. If so, I guess that is where the authority rests. But I won't bet the mortgage on this Congress doing anything other than jawboning and generating a lot of carbonic acid.
I think a smart candidate for president or congress could win on an “impeach the court” platform provided they are solid on other constitutional issues. I think Americans are waiting for a candidate to restore law and order to the Supreme Court.