I don’t post here often, but couldn’t think where else. And I am assuming that once a SC candidate has been rejected he would not be renominated later.
Since the right has declared they absolutely will not accept anyone the president nominates, why not find the top republican choices and nominate them? It would be a risk, they might approve anyway. And if they win the election and install one of their previous rejects there would be a fun footnote in history that he was an Obama nominee.