Almost. Hayes nominated Thomas Stanley Matthews but the Senate deemed the nomination in January 1881 as being too close to the end of Hayes’ term which was set to expire in March 1881. Thomas’ nomination was not voted upon and expired.
Garfield won the election in the fall of 1880 and was the President-elect. After taking office he resubmitted Thomas’s nomination after which he was confirmed.
Of course in this instance the election had already happened. But there is precedent for a sitting President not to have his nominee considered while we wait for the next president to take office.
There’s a good argument that the court should have an even number of members, since a case close enough that you need a tiebreaker probably shouldn’t establish precedent for the country. The lower court ruling can stand for the district in question, and a future case that’s more clear-cut can revisit the issue.
Of course, that works for cases under appellate jurisdiction. Not sure how an evenly divided court would work for cases with original jurisdiction. Bricker?