Sorry to keep harping on about the POD, but I've found out something very interesting which gives an incredibly easy way that Lincoln could lose one more state, causing the election to be thrown to the House, without the popular vote even changing at all in that state.
If you check out the votes in New Jersey for the 1860 election, you'll notice an anomaly: Douglas won the popular vote in the state, yet the state's seven electoral votes are split with four for Lincoln and three for Douglas. Why is this? Well, I found out why.
Background info: in New Jersey at the time, people didn't vote for the candidate -- they voted for the specific electors who supported a candidate. Now, at first the Democratic Party in New Jersey decided to put forth a ballot where people would vote for seven electors who would all vote for Douglas. But then they changed their minds, and banded together with the Breckenridge and Bell campaigns to create a "fusion" ticket in order to stop Lincoln. So the fusion ticket had a ballot wherein people would vote for three electors who supported Douglas, two who supported Breckenridge, and two who supported Bell. And should the fusion ticket win, the state's electoral votes would be divided accordingly.
Except, in one district the guy who was in charge of distributing ballots thought "fuck that" and distributed the Douglas-only ballots instead. Which meant that when people voted Democratic in that district, they were voting for the three Douglas-supporting electors on the fusion ticket plus four other Douglas-supporting electors. Meaning that the votes from that district put the three Douglas-supporting electors over the line, but split the anti-Lincoln vote on the other four elector slots and allowed Lincoln to take them with a plurality.
If the fusion ticket is distributed statewide, then Lincoln doesn't win any electoral votes in New Jersey. If he's also lost Ohio, then that brings his count down to 153 -- just short of a majority, meaning the election has to be thrown to the House of Representatives.
(Politics is fun!)