They still exist, but since the War of Northern Aggression there has been no GOP presidents or Yankee presidents but with support for slavery slipping to all time lows, and Nixon sucking as a candidate, this election became somewhat competitive.
Well I imagine without northern blacks voting it'd be a little easier than IRL. However, considering that the Republicans nominated an Irish Catholic for President that must mean that the Democratic Party might have more trouble winning states like New York, New Jersey, Connecticut, Massachusetts, and Rhode Island that shifted Democratic IRL due to immigration (and other factors). Do they counterbalance this by appealing to the American West and the High Plains where the rural folks live?
I'm guessing, and forgive me if I'm wrong, but based off of what I've read so far the average electoral map (assuming the Republicans never won an election since Lincoln) looks like this:
Where green represents swing states.
I assume, given the unpopularity of slavery, the map would probably be a lot more blue and green in certain areas of the country.