The chairman of the Republican Party in American Samoa, Utu Abe Malae, began feeling the pressure almost immediately: phone calls, commitment forms, anything the presidential campaigns could do, say or send to nail down his support as a delegate.

Ken Callahan, a district chairman for the North Dakota Republican Party, is perpetually fielding calls not just from the campaigns, but also from neighbors and friends who, excited by the process that is starting to unfold, are interested in becoming delegates themselves. “I receive, I would say, 10 to 15 calls a day,” he said, “and it doesn’t stop on weekends, either.”

And Holland Redfield, a Republican delegate and former lawmaker in the Virgin Islands, had a special call-in guest on his radio program the other day: Gov. John Kasich of Ohio, who promised more than just lip service to the islands if he became president. After years of being treated like second-class citizens by mainland politicians, Mr. Redfield said, “we are in the catbird seat. There’s going to be some hard bargaining.”