Are you saying that the people who became Republican weren't Whigs previously? Were there not two main parties, the Whigs and Democrats, before the Republicans? Some of the Whigs probably went to the Democrats, sure, but since the Whigs were mainly in the north, and the Republicans came to dominate in the north, wouldn't it make sense to conjecture that the base of the Whig party became Republican?
And although the Democrats split into several factions, Lincoln would have had enough electoral college votes to win the Presidency even if the Democrats only had one candidate. He swept the northern states, and in those states, even if you combined the Democrat votes, he still would have won.
What a third party would have to do is defeat Obama in states with 270 electoral votes. Take Texas for example. If Obama gets 38 percent in Texas, the Tea Party candidate would just have to carry 39 percent to win the electoral votes. Mitt could have the rest.
What tends to happen in these races is that the party that is in third place fades a lot at the very end, as people want to vote for one of the 2 candidates with a chance to win. If it is 33 to 20 between Tea Party and Mittens on October 15, you might see a lot of movement to Tea Party, and Mittens fade to 10. If it's the other way around, the opposite would occur. Either way, it can be enough to defeat Obama.
I am saying that the Whigs died first. The Anti-Nebraska party came next, eventually to be renamed the Republican Party.
If the Democratic party had something like a message, they might have won a few northern or western states. They didn’t, so they didn’t.