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YOU KNOW that an Argentine leader must be in political trouble if the subject of the Falkland Islands has come up again. In this case the beleaguered president is Cristina Fernández de Kirchner, whose populist administration in Buenos Aires has lost the support of most of the country. Hosting Secretary of State Hillary Rodham Clinton in Buenos Aires on Monday, Ms. Fernández de Kirchner requested that the United States mediate Argentina's dispute with Britain over the islands, which lie about 400 miles off Argentina's southern coast but have been governed from London since 1833.

Ms. Clinton responded by urging the two sides to talk, while wisely...