Say, for whatever reason, Abraham Lincoln (or whoever) doesn't win the 1860 presidential election -- most likely he falls just short of an electoral vote majority and the outgoing Congress then appoints someone else. As a result, southern secession is averted. Who would the Republicans nominate in 1864? How could this vary depending on who the winner is in 1860?
For what it's worth, without secessions the Republicans would have a plurality in the incoming House but not a majority -- the balance of power would be held by the "Unionist Party" (who seem to have been mostly non-Republican ex-Whigs with some unionist Democratic defectors). And the Senate would be majority Democratic.