It's the Prisoner of Zenda!
I haven't watched this yet, but a friend we showed Dave to thought it was borrowed from this. I think both were borrowed from the Prisoner of Zenda, written around the turn of the last century. All the prime roles of Prisoner of Zenda are represented in Dave and it looks like they did something similar here.
I strongly recommend the 1952 version if you want to compare notes.
Leewit
PS Since Dave came out at the beginning of the Clinton Presidency, barely, it might be a more a poke at the Democrats than the Republicans. Also, Kevin Kline is rather FDRish, which would make Sigourney Weaver Eleanor. We loved it and I would recommend it highly.