the words "embarrassment for"
But I think, at the very least, we're going to see some embarrassment for the United States, when some of the stuff that the CIA was, in fact, doing in the first years after September 11th are revealed publicly, and that's going to, I think, be quite controversial in other countries.
What is "some embarrassment for the United States"?

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It means the USA will be embarrassed. Look up the word embarrassed in the dictionary too.

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thanks

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May I also suggest that you send your question for corrections also , so that your sentence structure can be corrected as well , it will help you ,and will get your question answered at the same time . Just a tip  , ha ha , have great day . Ian

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"To be embarrased" is the verb form.  Embarrasment is the noun.

To say that "there will be embarrassment" or "embarrassment was caused by..." is the "passive voice".

This  phrase alone:  "There will be embarassement for the U.S."   tells us who will be embarrassed, but does not tell us who (or what) caused the embarrassment.