As they sought to revise and fine-tune the draft plan, the administration opened it for public comments. That tapped different voices in those states.

Residents of coastal communities feared that drilling in the Atlantic would bring a repeat of the 2010 Deepwater Horizon disaster in the Gulf of Mexico, which killed 11 men and sent millions of barrels of oil spewing onto beaches.

Mayors of a handful of small coastal communities assembled to pass resolutions asking Mr. Obama to take the Atlantic out of the drilling plan, sending those resolutions to the Interior Department. Environmental advocates began to organize aggressively. One group, Oceana, contacted mayors up and down the coast, urging them to pass similar resolutions.

“We thought, maybe we could replicate this and scale it,” said Jacqueline Savitz, a vice president of Oceana. “And then we started seeing numbers like 30 resolutions and 50 resolutions.”

Eventually, more than 106 coastal cities and towns in the coastal states enacted similar resolutions. Oceana teamed with regional groups, including the Southern Environmental Law Center. The groups covered lawns and beaches with “No to drilling” signs, but focused their attention on pushing through municipal actions that would resonate in Washington. They also worked behind the scenes to coordinate several anti-drilling opinion pieces in local newspapers from Richmond to Charleston.

In November 2015 and January 2016, Oceana arranged for several local coastal government and business leaders to travel to Washington to meet with White House officials, including Mr. Obama’s top environmental policy adviser, Brian Deese, as well as with Abigail Hopper, the director of the Interior Department’s Bureau of Ocean Energy Management. At the January meeting, Ms. Savitz presented the officials with a thick binder of the municipal resolutions, covered with a map highlighting all the towns that had passed those resolutions, dropping it on the desk with a thud.

Frank Knapp, the president of the South Carolina Small Business Chamber of Commerce, was at those meetings. “It was clear that while they had heard from the governors, they hadn’t heard from the smaller local groups,” Mr. Knapp said. “I talked to them about the threat to our tourist economy.” In particular, Mr. Knapp stressed to the officials that even the process of seismic testing, which uses blasts of sound underwater to determine whether there was oil and gas, could distress coastal residents.