Perhaps the fact that the government literally moves around with every election would lead toward a tendency for larger states? I kind of agree that the original colonies could keep their claimed territories, then you could throw in Louisiana, Texas, Alaska, and Oregon, followed perhaps by some version of Deseret (a cliche, I know) or maybe even the full Arizona territory and the original Mexican version of California. As for parallels with the actual HRE would we see the more developed cities attempting to gain autonomy as city states?
I see it as a potential for smaller states to hold more governments, because if each electoral council of each state gets to vote on who the President will be and so the State government will be held in, the most powerful and influential of the time would gain the most support? As I said to brickhouse, the Courts and Judiciary will be extremely influential across this version of the USA in my opinion, but economics are extremely important as well. When the Slave Trade still becomes a sad reality, that is all just business investments of the States involved and because of their greater independence from a centralised government, they keep the majority of income with increases in trade and bank importance.
That's where I see a Civil War still taking place but this time (possibly later on than OTL), not over the morality of slavery, but over the economic trade hubs of the South wanting Habsburg-style domination over the title, another collection of States seeking to keep the democratic "first amongst equals" system they're going with, and others just wanting independence and out of this potentially broken system.
In terms of these States, on the note of immigration, I would imagine that each state would probably keep more to their cultural roots than in our USA where English dominated apart from States near Mexico where Spanish is prevalent (but not as prevalent as English). The upper class would all more than likely speak English for ease of trade and discussions amongst all the States but the lower classes - i.e. the majority of people - would still speak French in Louisiana, Spanish in Florida, Russian in Alaska and so immigrants from the rest of the world would feel more included and get the right opportunities in these States. This leads to the identities of each State creating tensions in the Union where wars in Europe could have more indirect affect on the USA.
City States? Love 'em! I would totally see some cropping up on highly defensible, important trade routes like along the Mississippi River, the passages through the Rocky Mountains, and across the Great Basin. Your thoughts?