Conservative activists from around the country are gathering in Washington on Saturday, seeking to continue their momentum in shaping the national debate on everything from health care to White House staffing.

The demonstrators, who plan to march up Pennsylvania Avenue to the Capitol, are drawing their passion not from Bush-era fights over terrorism or gay marriage, but rather from Reagan-era debates over big government programs. The event comes on the heels of antitax events, dubbed tea parties, in April, and a series of...