well if you follow RSS on twitter it is your problem. If you follow people who share links, than it is a way better than RSS, because human filter is applied and you are more likely to get an interesting content.
But fair enough, the project looks nice. I'd only suggest to implement caching better:
1) Make /get_user_feed.php return only list of stories. E.g. [http://.../story1, http://.../story2]
2) Fetch stories one-by-one using unique links, set proper caching headers
You could also use pro.embed.ly