Hard to put it in the right order, but basically a federacy of cities and non-populated areas.
National government consists of a unicameral legislature (non-parliamentarian), a courts system, and a small gendarmie. Each city gets a single representative at Senate. Not quite liberum veto but some high percentage of the body required to make something law. The legislature and courts are defined in individual charters, if something crazy happens new organizations can be made in the same manner. The only other thing the national government covers is a base civil/criminal code, and the administration of it in the non-populated areas and in cases spanning cities by the national courts. Judges appointed by legislature.
Cities can do whatever they want. The only important limits I can think of are not arbitrarilly depriving someone of life or freedom of movement.
An Anonocracy.
Foreign and domestic issues are decided by whatever memes are popular on a rotating list of image boards.
The Great Fursecution will begin directly after the Revolution.
Tits will be shown, or deportation will ensue.
Mud huts and grass skirts.
Rule by paternal lineage.
No one lives past 40, but they live well.
Unicameral legislature chosen by a cumulative voting system. Mostly-powerless President assigned by the legislature whose main job is attend state funerals. The Supreme Court remains as strong as ever. Supreme court justices are chosen in a vast free-for-all MMA fight to the death and remain in power for life or until their assassination (which will be legal as long as it is not state-sponsored).
National government would consist of a strong Presidency led by an Admiral, General, or other qualified official, for a term of five years.
Parliament would be unicamberal, and each province would get one reprisentative.
There would also be a branch similar to the Republic of China's Control Yuan that monitors the government for efficiency and combat corruption.
Citizens must understand the laws that they are about to pass, and the candidates they are about to elect, before they are allowed to vote.
I'm a fan of parlimentary rule and proportional representation. That way you have actual choices in an election, rather than getting scary right wing or slightly less scary right wing. Don't kid yourself, compared to Europe, Americans get a great choice, conservative, or let's fuck the poor conservative. Europe has multiple parties ranging from outright communist to religious and nationalist parties. So they can choose the government that best fits them, while we choose the government that doesn't scare the shit out of us.
As for national leadership, I'd do it the way the founders intended -- first place finish makes you president, second place makes you vice president. At least this way the next GWB will have to listen to an opposing view when he tells the cabinet that we'll be greeted as liberators when we invade Iran.
In both cases, if you can get enough signatures to be one the ballot in all the regions you'd represent, you debate. Imagine having to listen to Greens and Libertarians as well as the traditional two parties.
The judiciary wouldn't change.
Theocracy.
As in god actually comes down and runs the country for us.
Whatever has the fewest furries.