Oh they can be impeached, all right. After all it just means "accused."
It remains for the Senate to convict and punish, but since the passage of the 17th Amendment, that step is almost meaningless, specially in the case where each party holds a subbranch of the legislature; and guess who has the final word as to the Constitutionality?
Sure the House could impeach - and the Senate even convict and punish - but not under the auspices of our Constitution.
They would be forging new ground - ground far from our Constitution- in arguing that five of nine (or more) SCOTUS Judges agreeing on a ruling of law is a “high crime” or “misdemeanor” or that disagreeing with the President is not exhibiting “good behavior” consistent with being a Judge.