BEDMINSTER, N.J. — The local roads were closed, with Secret Service agents, the state police and local law enforcement on patrol. Deep in a protective bubble, President-elect Donald J. Trump was holding court in his living quarters not long after his election, receiving would-be members of his future administration at his country club. A crush from the news media waited outside for a photo opportunity. But there was little traffic, no protesters and few gawkers — except for a herd of horses, idly chewing grass.

This seat of presidential power is far from Fifth Avenue and its gold-hued Trump Tower, and farther still from Washington and the White House. It sits on a golf course in Bedminster, a rural New Jersey township of just over 8,000 residents, where small farms and crumbling Revolutionary War-era structures abound. This sleepy pocket of the state, where residents boast about their miles of dirt roads, has suddenly found itself in the glare of attention as the home to Mr. Trump’s weekend getaway and the headaches that may come with it.

A few days before Christmas, Representative Leonard J. Lance, a Republican who represents the area in Congress, sent a letter to Attorney General Loretta E. Lynch requesting a grant to help Bedminster pay the cost of protecting Mr. Trump when he is at his country club. As Mr. Lance put it, the golf course could become “Camp David North.”