The tea party has emerged as a potent force in American politics and a center of gravity within the Republican Party, with a large majority of Republicans showing an affinity for the movement that has repeatedly bucked the GOP leadership this year, a new Wall Street Journal/NBC News poll has found.

In the survey, 71% of Republicans described themselves as tea-party supporters, saying they had a favorable image of the movement or hoped tea- party candidates would do well in the Nov. 2 elections.

Already,...