Just Words, Just Speeches.

dic·tion
1. Choice and use of words in speech or writing.

President Obama famously made a Big Deal about the words people used in making political speeches. Later, he said that some Americans are the enemies of other Americans, solely on the basis of their political opinions. Now he says "er, hum, uh, what I meant to say, uhm, uh, was that, (idea finally forms) we are opponents. Yeah, that's it, opponents. Right.*"

News flash: When you call someone your enemy, they might tend to think, e.g., that you consider them to be an ENEMY. As the President of the United States, that means you think the people of your nation are enemies of the State. In case you forgot, this is what one does with an enemy in the common use of the word.

en·e·my
n. pl. en·e·mies
1. One who feels hatred toward, intends injury to, or opposes the interests of another; a foe.

op·po·nent
n.
One that opposes another or others in a battle, contest, controversy, or debate. See Synonyms at enemy.

Are they synonymous? Yes. Are both appropriate for the President to use in this context? No, which is why he backpedaled when the news finally reached him that the People were offended. Is it his fault anyway? No, of course not. Ol' Tennis Match was merely reading what someone else wrote for him to read off a TelePrompTer. The leader of the free world can hardly be expected to be held accountable for his "just" words, after all!

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*this may not be a direct quote
Definitions from the American Heritage Dictionary of the English Language, 4th Ed., emphasis mine.