And if you can set limits on what journalists write and broadcasters say, you can shape what people think and believe.
What's key is that the limitations can shape people's thoughts and beliefs. Not, necessarily, arguments. Most people who support gay marriage couldn't defend their support intellectually if their life depended on it, beyond droning some bumper-sticker slogans. (Frankly, many people who oppose it are in a similar boat.) More than that, if the cultural winds started to change, I'm willing to bet a good number of those who support it would stop due to that change in climate alone.
Public piety is exactly that - public. For show. Just as you have 'nominal Christians' - Christians in name, even Christians in some practice, but for whom ultimately a kind of watered-down and non-reflective faith at best obtains - you have nominal leftists. People who choose their words carefully, who will say the right things if probed and even vote the right way, but who are ultimately are pretty blase about the whole thing. If in the next five years gay marriage were portrayed in popular culture as a joke or morally offensive, these are the people who would react by changing their minds to reflect the new mood, not by standing their ground and defending their ideals. Because they have fewer than most think, and fewer than even they think.
Which isn't to say that there aren't determined leftists out there, just as there are determined Christians.