Poll: North Korean concerns at all-time high

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Still, only 46 percent of Americans believe the crisis will be resolved by diplomatic or economic means alone, while a majority disagree.

"If North Korean leader Kim Jong Un wanted to get the attention of the American public, his strategy is starting to work," said CNN Polling Director Keating Holland in a statement. "The 41 percent who now consider North Korea an immediate threat to the United States is up 13 percentage points in less than a month."

The survey also found strong support for an American response were the North to follow through on a threatened attack of South Korea. Of those surveyed, six in 10 said they would support the U.S. responding militarily.