Grant Pulls a Sherman

What would happen if in 1868 General Ulysses S Grant stated that he would not accept the nomination of any party nor the office of President if he was elected? Who are the most likely (Or most interesting Dark Horses) candidates for the Republican Party without the Hero of Vicksburg and Appomattox?

John Fremont?

I don't know?

Errr....I tried a timeline on this. There was possible politicking to have George H. Thomas elected, which I did. It ended in that I made it too ASB.
But there were calls in Ohio and other states from men who had served under him to put him on the ballot. He declined. But, it could be possible.
He had a stroke in 1870, but it may have been caused by answering a letter, and if things had involved him not answering it...