It is certain that Keeler/Logan is a republican ticket. In season 3, known democrat Palmer was going to debate senator Keeler, so Keeler would have definetly been the Republican debating the democrat. So when Palmer dropped out, and according to the website Keeler beat Prescott (the slimy Vice prez from season 2).
And yet the republican president kept on board a staff member from Palmer's administration. They definitely are playing to a non-partisan image of the Presidency (which actually is kind of nice for this show).
I stopped watching during season 3, so I missed this presidential election.