Apparently that was a favorite expression of my grandmother, usually in response to some suitor for one of her several daughters. And at least according to Nate Silver, it might apply to Senators, too -- the notion that you should just shut up, because the more you talk, the less people like you. He looks at the varying fates of Max Baucus and Jon Tester -- both Democratic Senators from Wyoming, but one of whom (Baucus) decided to make himself front and center during the health care debate and has seen his approval ratings drop 20 points, while Tester simply shut up and still has very high approval ratings. Now, to be fair, there are a lot of other mitigating factors, most notably that Baucus was chair of the committee that needed to pass health care, but still, he didn't exactly shun the spotlight.
In general, I think politicans over-estimate how much the public cares about their particular positions. Rather, a lot of the time, the public just gets tired of hearing about a given politician, and thus sours on him or her. In other words, just stop being a horse's ass and do your job without me having to hear about it.