Andrew Johnson as VP

[wpbinzel]

To add to what the others above have said, keep in mind in the era between Andrew Jackson and Abraham Lincoln, political parties came and went (for example, Whig, Know-Nothing, Free-Soil, etc.) The newly formed Republican Party put up a candidate for President for the first time in 1856. So, in 1864, there was no long tradition of running under that name, and in an effort to garner broader political support, Lincoln and Johnson (a pro-Union Republican and a pro-Union Democrat, respectively) ran, as Roger pointed out, under the banner of the National Union Party.