Actually, the Supreme Court today negated the House Impeachment charge of Obstruction of Congressional Investigation by granting judicial review of the multiple lower court cases brought against Trump about his tax returns etc. Since the Court accepted review they essentially ruled that the Executive is entitled to Court review in disputes with Congress.
So then impeachment, if it occurs, could be ultimately overturned by SCOTUS if the House was deemed by them to have ran roughshod over other parts of the Constitution.