For years, when Republican state senators met privately in their elegant, high-ceilinged conference room in the Capitol, most senior members clustered around the room’s center table, close to Joseph L. Bruno, the majority leader. But Dean G. Skelos, the hard-driving Long Island Republican and deputy majority leader, sat in a back corner. From there, he studied the scene, taking in members’ facial expressions, their tones of voice and their reactions to other senators’ ideas. “My grandfather taught me a long time ago, be a buyer, not a seller,” said Mr. Skelos in an interview on Thursday. He added: “I like...