In The Power Game, pulitizer prize winning journalist Hedrick Smith promulgated what he called "the iron law of politics." In a nutshell, he says if you have some control and desire influence, narrow the circle of those who give input on an issue. If you have no power, do the opposite - expand the circle.
(Here, for example, is a link showing the various chapters, one of which is called "The Power Loop: Narrow Access vs. Widening the Circle")
Opening the circle, he explains, increases the number of actors and decreases the portion of power that any one actor can exercise without overruling the "consensus." Anecdotally, lobbyists use this rule in practice. Tax minutia that may deliver a big break to particular entity is rarely trumpeted - unless if the tax break is running against a strong headwind. Then the "oh look at who is stopping American Business (TM)" arguments come out. Conversely, if someone wants to scupper the whole thing, it becomes a "loophole for the rich."
Expanding the metaphor to "interest groups" and "public opinion at large" is easy, because lobbyists are, in fact, just representatives of an interest. The difference between an "Interest Group" and an interest is nothing but scale. Nobody is going to sneak through an massive anti-abortion or gay marriage bill, for example, but the strategy of going state by state in each instance proved far more effective than national attempts in either event.