Lots of people gave their lives for people to be free to call their democratically elected leader "dude". Unless you're interacting with the president in a professional context, it shouldn't matter at all what you call him (barring certain epithets and "Hitler").
How about "Your Dudeness" or "El Duderino", if you're not into the whole brevity thing? Petty namecalling is stupid, but "dude" is a sign of (modest) respect.
Seriously, as a foreigner I reckon that the office of the President of the United States needs to be taken down a few notches. I mean, I accept that the dude needs a private jet, but does it really have to be a 747 and called Air Force One? I accept that the dude needs a limo instead of driving himself around, but does it really need to be a custom-built limo? I accept that the guy can have a nice executive mansion, but does he really need his own seal, his own theme tune and a standing ovation every time he shows up to talk to Congress?
There's a difference between the need for more civil discourse and the need to address people by their titles. Uncivil discourse is unproductive, but I don't think "dude" is particularly uncivil. "King George" is.
