YORK, Pa.—Trying to plug a $3.8 million budget gap, the York Suburban School District, in the rolling hills of southern Pennsylvania, is seeking to raise property taxes by 1.4%.

No way, says Nick Pandelidis, founder of the York Suburban Citizens for Responsible Government, a tea-party offshoot, of the plan that would boost the tax on a median-priced home of $157,685 by $44 a year to $3,225.

"No...