Yes, but the key difference is that the states that comprise the USA don't act as their own, sovereign nations. Imagine if California and Texas, for example, were independently represented in the United Nations, had independent economies linked only by a shared currency, and listened to the federal government only when they felt like it? That's more along the lines of what the EU is.
The USA made the conscious decision to be a unified, federalist nation. The EU is "trying to have its cake and eat it, too" in that it won't go that far. It wants the benefits of federalism with the benefits of independent national sovereignty. What it gets, instead, is neither one nor the other.
Agreed, and I'd like to point out that the USA did attempt a form of loose federation under the Articles of Confederation. It didn't work very well, and although it took a lot of cajoling to convince the various states to submit to a federal authority, it has worked much better.
The USA made the conscious decision to be a unified, federalist nation. The EU is "trying to have its cake and eat it, too" in that it won't go that far. It wants the benefits of federalism with the benefits of independent national sovereignty. What it gets, instead, is neither one nor the other.