Are we sure Daniels is a Democrat? I thought Palmer was a Democrat, which would make Keeler a Republican (and by association Logan and Daniels as well).
W. Palmer would likely be a Democrat (as his brother was) making Daniels a Democrat although it wouldn't be out of line for him to pick the Independant -but right leaning- Daniels as a running mate. Which would make this lady a Republican which doesn't seem to follow since, ahem, her concerns over the S. African nation that has no resources to exploit doesn't follow the ideals of her party.
David Palmer was a Democrat. This was established, in stone, in the first season.
Keeler ran against Palmer in S3 making Keeler a Republican.
Keeler is killed in S4 making Logan the President, a Republican (or possibly a Independant.)
Wayne would've ran against Logan's replacement Hal Gardner (who likely would be a Republican.)
Wayne's VP was Daniels which I guess would make him a Democrat and this lady a Republican.
I think it's more likely that much like the year/"perpetual now" that the Presidents don't belong to any paticular party affiliation.