It’s easy to compared countries like Ireland and Greece to US states and conclude that the sovereign debt situation in Europe has a US analogy, but it’s not a clean analogy.
For one thing, as PragCap points out, the US does have a common Treasury and an established system of transfers between states. To advocate a complete separation of finances from one state to another, as if they weren’t part of the same country, is to deny reality for political purposes.
Another huge difference is that in the US, a crisis at the city or state level, wouldn’t precipitate a banking crisis. If Illinois were to default, it wouldn’t necessarily precipitate a run on banks in the state of Illinois.
This isn’t the case in Europe.
This chart from SocGen makes very clear that in Europe, the perceived credit risk of various banks is tightly linked to the credit risks of the countries in which they preside. That magnifies the risk significantly, and truly creates a notion of systemic risk. In the US it’s conceivable to have lots of defaults without a follow-on systemic crisis.