In the Hollywood Reporter noted playwright Tony Kushner, who wrote the screenplay for Steven Spielberg's Lincoln, states our 16th President would be a Democrat today:
The Republican party today has turned into a group of people who don’t actually believe that government is a good thing. You can’t have any connection to Abraham Lincoln if you think that. Lincoln was a lawyer who had a profound belief in the conviction that government was a great blessing for humanity, and certainly wouldn’t have read Ayn Rand. He wouldn’t have had any interest.
Actually, Tony, if Lincoln were around today I think he'd stay away from the theatre.
But Kushner's not alone. Historian Doris Kearns Goodwin, who wrote the book the film is based on, also says Lincoln would be a Democrat. Some of the evidence:
[Lincoln] believed government had a role in helping people rise to the level of their talent in their discipline, that sort of equal opportunity role, in that sense he might find the principles of the Democrats congenial.
This is why leftists like Kushner and Kearns Goodwin embarrass themselves when they engage in such speculation. They not only suggest their understanding of Lincoln is shaky, they show no understanding of today's Republican party.
In addition to being transparently partisan, the game they're playing is pointless. It's easy enough to claim or disavow any historical figure. I can show you how Hoover and Nixon were Democrats while FDR and JFK were Republicans without breaking a sweat. The truth is the parties have changed tremendously over time, as have general political beliefs, so it's hard to compare then and now with any specificity.
For instance, today's Republicans, by Lincoln's standards, believe in a government that is almost unimaginably vast. (Please let's go back to the size of government in Lincoln's day--or even FDR's.) Meanwhile, the way Lincoln talked about religion he might be called a theocrat today, while Republican's views on race relations would make them radical leftists by the standards of just a few generations ago.
So basically the Kushner/Kearns Goodwin arguments breaks down to "Lincoln good. Democrat good. Lincoln Democrat."