Basically, the field of linguistics needs seriously help in the public relations front. And I am certainly no angel when it comes to this....
But, the sad truth is that linguistics are sitting on topics that absolutely fascinate people. When I take the time to REALLY start talking to people about language, I find versions of the same questions that perplex linguistics today. People are generally fascinated by language in all of its aspects.
Yet, in the public eye, most of the discussion is not about language as linguists see it. Rather, the public view is that language is mere communication. That language is nothing that special (i.e., dogs have it too). Or that language is just that hodgepodge of rules and exceptions taught in sixth grade and preached by the mavens slowly slipping to hell in a hand-basket.
This is obviously a problem.
The bigger problem is that it seeps well beyond the public but into institutions of higher learning and scholarly research. Even among the highly educated, basic knowledge of linguistics is uncommon. This hurts the field in too many ways to count (funding, general institutional support, etc.).
But it doesn't need to be this way. Linguists are sitting on a gold mine, we just need to start mining.
To me, the key is a refocus on undergraduate education (perhaps with some of the wiser, more press-enabled folks working that angle). Linguistics departments need to find ways to make survey courses the types of courses that students want to take and the types of courses that will stick with students. There's obviously a lot there: there is a wealth of potential materials in popular culture that is just waiting to be mined.
Such attempts would of course increase the majors. But that's not the ultimate goal necessarily. We don't need to triple the size of the field. Rather, we need the public and the future university administrators looking at linguistics from anywhere but a place of ignorance.