Imagine if the shoe was on the other foot: If a president was at the beginning of their term, a justice died, and the President decided they were happy with the new balance of the Court and flat out refused to nominate anyone to fill the vacancy (possibly hoping for a more favorable Senate after the midterms), what would happen? Because I think congress would be well within their rights to consider impeachment.
Well, it
might, MIGHT be unconstitutional but that doesn't necessarily make it illegal, no? Lawmakers from time to time pass, or try to pass laws/regulations they know are unconstitutional beforehand and never get in trouble. So, as I understand it, the president has to be convicted of 'high crimes and misdemeanors', which forgoing a nomination is neither.
However, the only reason I can think of him leaving the spot empty is if he knows he can't get a super liberal justice confirmed despite him really wanting that for whatever reasons, so he just doesn't nominate anyone, hoping the Senate composition will change by next election. It would be much easier to just keep nominating people they know will fail, though.