Really? Tell me, what happened to Judge Garland's nomination to the Supreme Court?
They have the power to not approve a nomination thus preventing that person from taking the appointment. If they refuse to approve any then he can use recess appointments.
He could also appoint the pseudo cabinet members like Obama did when he took over.
It is a tremendous breach of the authority of Congress for them to say "keep this person or you don't get anyone". Hardly something a supporter of the Constitution would endorse.