No major American political party has nominated a full-throated socialist for President. But after his strong showing in Iowa, could Bernie Sanders be the first? That’s the question Democrats have to ask as Tuesday’s New Hampshire primary approaches. Republicans may want to hold the Schadenfreude.

The counting fiasco has muddled the Iowa results, but it seems Mr. Sanders has either finished a narrow first or a close second to former South Bend Mayor Pete Buttigieg. The Vermont Senator now leads in New Hampshire by 4.7 points...