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The question of how binding ACTA is results from a back-and-forth about how much damage ACTA can do to copyright laws in the U.S., since the government position on it is that it doesn't require any changes to current domestic law. One reply to that is that, even if the laws we have on the books now comply with ACTA, signing ACTA can prevent Congress from rolling back those existing laws in the future. If it did so, we'd be in violation of an international agreement. So agreeing to ACTA could lock our often-imbalanced copyright laws in place.
The State Department letter basically confirms this, saying yes, the U.S. would be "bound under international law" to keep its laws in line with ACTA. But, as the letter goes on to point out, that doesn't actually prevent Congress from going ahead and passing new laws inconsistent with ACTA. And those new laws would be perfectly valid and enforceable in U.S. courts. ACTA, on the other hand, isn't enforceable in U.S. courts, since it doesn't have the authority of law here (see the "Bonus pedantry" section below for an explanation).
Now, this doesn't mean that everything is copacetic—this would put the U.S. in violation of ACTA. But that violation isn't anything that gets applied directly in court here—a copyright holder couldn't sue a defendant for violating ACTA. Instead, the complaints about the U.S. not keeping to the terms of its agreement would likely come from other ACTA-signing countries. What would happen then isn't particularly clear—there's no specific venue in which the countries could make their arguments, no world court at which someone can be sued for "violating ACTA." Instead, what happens is that some countries may, at the insistence of some of their industries, might try to bring trade pressure to bear upon the U.S.
That's by no means a good thing, but when people ask whether or not ACTA is "binding" upon Congress, they seem to be asking if it would prevent Congress from passing future laws. The answer to that is no.
What ACTA does do, however, is indicate to the world that its signatories are bent upon establishing (and in some countries, raising) minimum penalties for copyright, patent, and trademark infringement, and that any net negatives of IP aren't a particular concern among national governments. It also reinforces a political atmosphere internationally of expanding copyrights, making it harder to move the dialogue into the future. It doesn't, however, prevent Congress from exercising its constitutional powers and passing contradictory laws; it just makes it politically harder to do so.
Bonus pedantry: There's a similar amount of confusion about whether or not ACTA is a "treaty." The answer depends upon what language you're speaking. If you're speaking U.S. legalese, the answer is no. If you're speaking international legalese, it's yes. That's because the U.S. has a specific constitutional definition of "treaty:" a treaty has to be signed by the President "with the advice and consent of the Senate." And in U.S. law, a treaty can supersede previously-passed treaties and previously-passed domestic laws. ACTA, however, didn't get Congressional approval, and in the U.S. is classified as a "sole executive agreement," which means it’s an agreement that the President has made with other countries. It can't, under U.S. law, create or change existing laws; it's just a promise the President makes on behalf of the country to other countries.
In the international context, though, the word "treaty" means something more general. For instance, the Vienna Convention on the Law of Treaties (which the U.S. has signed), a treaty is just "an international agreement concluded between States in written form and governed by international law." ACTA does fit that definition, which is why you'll see lots of people (mostly in other countries, but also in the U.S.) refer to ACTA as a "treaty." They're not wrong to do so; they're just operating within a different framework.