I would love to go through a primary season prior to the main campaign. To me, primaries would seem more difficult, because you're competing against 6 or 7 members of the same party as you. This could make charisma, comeliness, etc. much more important than they are in the general election. Also, when picking your running mate, picking someone who captured certain states in the primaries could help you pick up those states in the general election, regardless of whether the VP is from those states. Also, naming a running mate that had already run in the primaries would mean the running mate already had a lot of awareness still spread out throughout the country, and the running mate's awareness and support could be merged into your own.
I would also like to make custom maps. One map I'd love to play is the Confederate States of America. The 1861 election would be like a counter to the 1860 US Election scenario already present, and this map would bring a large new cast of characters in, like Jeff Davis and other Southern politicians. Or, you could delve into alternate history and hold CS Elections well into the 20th century - if you've read the works of Harry Turtledove, you know what I mean.
The custom maps would lead into a custom scenarios idea. The player could create a list of issues, choose their icons from a given pool or use custom ones, choose which party is on which side of the issue, etc. That way, the player could set up elections in almost any election year in the nation's history. To really do this effectively, of course, the custom map tool would be needed, to at least set the number of electoral votes each state has, which of course differ every few elections.