Yeah it's an interesting one.
For starters, Arnie isn't a hardcore Republican, his renewable energy, hydrogen fuel and emissions policies for starters have brought him into conflict with his party. Also the federal/state system is very different, in terms of taxation and general policy - people may not object to policies at a federal level but on a state level may prefer the Republican model.
The model of government is something which is often forgotten about the US, for all its faults it is very democratic with the Federal/State/County/Incorporated City system, with elected officials and public involvement at every level.