Only three weeks have passed since the end of the tea party-inspired government shutdown, yet already the group's citizen activists find themselves in the eye of another political storm. Republican-oriented business groups like the Chamber of Commerce and the National Retail Federation are now threatening to challenge tea party-favored primary candidates, especially if they appear to be in the Ted Cruz scorched-earth political mold.

These business interests and a growing number of GOP insiders are fed up with tea party tactics...