The EFF and the ACLU are fine for what they are, but they've got too broad of a mandate to have the kind of focused impact you want. You can't be an effective mainstream advocacy organization when you're off defending unsympathetic people for principled purposes. That's an important thing too, but it's a different thing.
For people interested in effecting real political change, I seriously recommend watching this documentary on the Prohibition: http://www.pbs.org/kenburns/prohibition. One group of people got a nation that until (and during and after!) prohibition drank 140 million gallons of liquor a year to outlaw alcohol. The money wasn't on their side (the government made 1/3 of its revenues from liquor taxes and the beer makers had tremendous power), but they accomplished their goal by masterful politicking: http://en.wikipedia.org/wiki/Wayne_Wheeler.
"Under Wheeler's leadership, the League focused entirely on the goal of achieving Prohibition. It organized at the grass-roots level and worked extensively through churches. It supported or opposed candidates based entirely on their position regarding prohibition, completely disregarding political party affiliation or other issues. Unlike other temperance groups, the Anti-Saloon League worked with the two major parties rather than backing the smaller Prohibition Party."