Congress confirmed Gerald Ford as VP, and then when Nixon resigned, Rockefeller as Ford’s VP. I am not aware of any presidential appointment power, other than to nominate a replacement for Congressional approval. But it’s moot. By the time mid-terms are over and the new Congressmen installed, Foe will no longer be coherent enough to do or say anything, let alone go through the motions of appointing Xi Jing Pig’s selected replacement. He’s declining rapidly, will have to be 25th-ed or heart attacked. Mitch is POTUS by default.
Of course it's likely that before that, dems could bribe Romney, Murkowsky, etc. to avoid a tie. They don't want to wait until after the midterms and a new congress is sworn in.