“Everything about this movement is momentum,” said Mr. Sky, 27, an Internet consultant from the East Village. “We need to show people that we are still relevant.”

Since the earliest moments after they were displaced on Nov. 15, many protesters drifted north to the park at Canal Street and Avenue of the Americas. Trinity embraced the wandering drifters and ministered to their needs. But when the Occupy movement expressed an interest in setting up an organizing camp in Trinity’s private space, beside the public park, the church said no.

So after some protracted debate, the Occupy Wall Street forces aimed their skills on the church.