Thm. Jefferson, while president, tried this very thing with Justic Samuel Chase of the Supreme Court, with Chief Justice John Marshall clearly in the cross hairs. Thank God Jefferson failed...to his towering fury, I might add.
Jefferson and the rest of the Republican/Jeffersonians felt that the SC had no business deciding on and/or over turning laws passed by the (Republican/Jeffersonian) congress who claimed they spoke for "the People".
The role of the SC was to be, in their view, essentially to serve at the pleasure, and for the purpose, of the party in power- namely the Republican/Jeffersonians who felt that with the manipulation(s) of the SC they would maintain a lock on power; as they probably would have for several elections, if not longer.
Mercifully, when it came to a vote the sense decency, statesmanship, and of duty called forth "the better Angel of our nature" in enough members of Congress, including a surprisingly large number of Republican/Jeffersonians, to defeat the measure of impeachment against Samuel Chase...and any other Justice, at any other time.
So why was no amendment passed? Oh, several reasons, I expect. The shame a lot of the members of Congress felt about getting tangle up in this mess ("Damn your conscience! Vote with your party!"); the sullen fury of Jeffereson who most certainly would have pushed for an amendment if he thought he had even a ghost of a chance; the mounting troubles with Britian; the trouble brewing out West, etc.