Do any of America’s enemies ever try to place blame on the United States for natural disasters, (perhaps saying that America is “somehow” responsible)?
Do their people ever tend to believe these accusations?
It happens all the time. I remember a couple of years ago a large lake in Russia mysteriously vanished overnight. They interviewed one of the people who lived on what used to be the shore of the lake, and they said that their first thought when they woke up and looked out and saw no lake was that the Americans had done it. And this is after the cold war, when we’re supposed to be at peace with each other.
A lot of folks in the middle east believe the big tsunami was caused by America and Israel, either through accidental nuclear testing or intentionally with nukes.
A lot of earthquakes in the Middle East and Asia are blamed on secret American “superweapons” which are designed to wreak havoc on Muslims.
I’m sure there are lots of other examples out there as well. Not everyone believes it, of course, but a quick scan through the internet reveals some rather scary insights into how some people think.
There were a lot of American Evangelicals blaming Katrina on Americans, mainly gays and their supporters, and the other evil denizens of New Orleans.
As for whether these people are “enemies of America”, well, I’m not going to go there. 
When I visited the Museum of Communism in Prague last year, there was an exhibit saying how the Communist Czechoslovak government blamed the US for an infestation of potato bugs at one point.