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Europe is in love with Barack Obama, according to recent polls. But will this affair of the heart be a brief flirtation or something more enduring? Like many relationships, the partners themselves may not really know until times get tough. With troubles looming in Afghanistan and Iran, that day of reckoning is fast approaching.

The United States would clearly welcome greater European help in Afghanistan. Although a majority of Americans are still optimistic about stabilizing Afghanistan, support for “Obama’s war” has been slipping. And recent allegations of President Hamid Karzai’s fraudulent election have caused even staunch conservatives like George Will to question the mission and argue against sending more soldiers. If Republican support for the war erodes, then Mr....