James Madison warned people about the dangers of this conflicting group. Today it is known as an interest group

Madison warned about a lot of things. I suppose you are refering to the warnings in Federalist 10, wherein Madison warned about factionalism developing of groups of folks worried about their interest above all. I would label the group lobbyists. Examples of groups worrying about self interest: US Chamber of Commerce, National Rifle Association, National Republican Committee, and so on.