If you want to get subscribers from facebook then you need to grow a loyal fan base within facebook. The easiest way is to create your own group, fan pages are hard to promote these days if you're not paying for Ads.
The simplest way is to keep adding new people to your group on a daily bases, offer them valuable content via a blog then use your blog to get them to subscribe by placing optin forms on the sidebar, below each post and using popups (I don't use them though).
Ask members of the group to invite friends then give them bonuses for their effort. You can even run a contest, whereby the person who invites the most amount of people gets a certain bonus. Facebook makes it easy by showing you who added the new member and when.
Upgrade active members to become admins and give them certain privileges over ordinary members. Let other members know that the more they're active they'll also get upgraded. Then ask your admins to help you grow the group. But don't stop offering valuable content and also create a dedicated squeeze page for collecting leads.
Maybe create a special squeeze page that say something like "for members of 'group name'..." or anything similar. Share the squeeze page in the group once in a while and mix it up with your blog posts and affiliate offers.
This way, you will have something that is for long term. This is traffic on demand, at a push of a button.
BUT! It's not going to be as easy as it looks, grow your followers gradually and soon you'll reap the benefits, don't rush and never give up.