In my opinion, (and this is my opinion only),

a.) the right has been very effective in outflanking the left when it comes to controlling the mass media, which is where most people get their news. (Be it TV, talk radio, internet, or social media). The lifting of the Fairness Doctrine and the removal of limited ownership of TV/radio/newspaper outlets has been exploited very well by those on the right. On the left, not so much. (Remember Air America?)

b.) Right wing voters are less nuanced in their selections. Their mindsets and allegiances tend to be determined and dominated by one or two issues, and you have a hard time convincing them that there might be a middle ground or compromise (or god forbid, they might be wrong). On the left, there appears to be a much less solid, more malleable allegiance.

c.) and relating to item b.), the dumbing down of the electorate due to over-consumption of anal-retentive right wing media offerings have reduced the right vs. left/red vs. blue dynamic to more of a sporting event type of mindset (at least to the low hanging fruit of the right wing tree). Gone are the days of a government that can compromise to forward the goal of bettering the country. Now it is a requirement to demonize your opponent and oppose everything they stand for, and minimize and dismantle their accomplishments, even if they benefit people.

To the right wing base, you can express your patriotism through bumperstickers, cute slogans and sound bites. Getting off of their ass to defend someone's right to free speech (that is different from their viewpoint) hurts their feelings and makes their brain cramp. They simply want everyone to be like them and think like they do. Then everything would be easier...

So, to answer your question on how to get them to see there is another side to the coin? Just keep trying. It will happen one person at a time, not in a huge mass movement. Point out the absurdity of someone's argument in private so as not to embarrass them in public. And realize that you will not be able to reach some people, simply because they are unfeeling and callous assholes.

Just my $.02.