The US is far more like the EU than it is like Britain or Canada, being a Republic of aligned States. We have a body representing the states themselves (the Senate, and each state is equal and gets 2 Senators), a body representing the People in those states (the House of Representatives, which has been capped for total size and is no longer equally proportional but serves the same purpose), and a body representing the entire Union (the Executive branch - the President, Vice President, Cabinet, etc.).