Are there any techniques to get this to happen? Most of the users just don't care enough about my product to go that extra step. Short of changing the entire product, what steps could I take to somehow gain fans?
1) Sent the first few tweets that explained who I and the company are.
2)I followed x number of people who looked interesting and relevant to my business. Many of them followed back (very few auto-followed)
3) I installed TweetDeck to sit in the background when I'm online (and not in do not disturb mode) - there are often questions or observations from someone I follow that I can contribute to. I reply, and so far, most times I do they tweet a thank you, and I get 2-3 signups within 10 mins from their followers.
4) When I get a new follower, I have a quick look at who they follow or who follows them, for new leads to repeat Step 2.
5) Next step is to Direct message all new followers. In your case, that might be linking to your Facebook page?
A note on Facebook pages - it takes me four clicks after I log in to access my own fan page. The likelihood of me doing that for any other business? Nil.
I had been running Facebook ads linking directly to my "Farmville Timer" iPhone app on the app store. Then I realized I was getting no network affects from that. So I set up a fan page and I'm now running ads asking people to become fans. That way I'll also get noticed on people's walls and feeds.