HARRISBURG, Pa.—Some day it might be remembered as the Tea Party primary.

The newly forming activist groups that identify heartily with calls for cutting taxes, deficits, red tape and government programs are organizing demonstrations, holding candidate forums and getting a boost from private conservative institutions in Pennsylvania.

Candidates, especially Republicans, who are running for office are heeding the message that is spawning challengers to GOP incumbents or establishment candidates.

There are dozens of the groups in Pennsylvania, some that claim hundreds of members. The goals and methods tend to vary from group to group, and some are able to provide few specifics as to how they want government to change, but they’ve made a strong impression.

But their refusal, so far, to endorse establishment candidates or form a third party may be their strongest hand. Some, perhaps many, tea party organizers want to remain independent and force Republicans, Democrats and independents to court them.