Twitter Streaming API

I want to use Twitter's Streaming API to collect all of the tweets of users signed onto my website - of course I would have an oauth token and secret for them, but I want to store their tweets as they make them. Is that possible with the Streaming API? If so, can anyone point me to some PHP library that will help me implement such a task? I tried looking in to Phirehose, but I don't understand how to use that library to get the feeds of all the users signed up on my website. Any help would be greatly appreciated.