Support for Donald Trump among Republicans has declined in the past month, leaving him slightly behind Sen. Ted Cruz in the GOP presidential race, according to a new Wall Street Journal/NBC News poll conducted after a combative debate performance that may have soured some voters on the New York businessman.

Mr. Trump had enjoyed a double-digit lead over his rivals, but the new poll found support for him falling by seven percentage points since mid-January. Among registered voters who said they would participate in a GOP primary,...