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“None of these things represent the test Vice President Biden suggested,” said Mr. Miller, who is working on a book about presidential greatness as a scholar at the Woodrow Wilson International Center for Scholars.

“None of them directly challenge American credibility or prestige in a way that requires an immediate response by the United States. It does reflect that we are being taken less seriously these days by our friends and our enemies.”

Mr. Miller said these challenges are likely to increase.

“You will see the limitations of American power demonstrated in the coming years in a way that is much less crisis-oriented,” he said. Referring to the Bush administration, he added, “For all of their toughness and vaunted capacity, there is a cost to failure.”