Partner providers of Twitter data, like Datasift and Gnip, have some more fine-grained options for digging into/tracking tweets.
Given the way that the Search service indexes tweets, I would never use the Search API in a case where you’re trying to track “all” tweets that match condition XYZ – you’ll almost always want to use a Streaming API for a scenario like that – but our Streaming API doesn’t support the ability to track on individual field values like this.
Since you’re already using the Search API and might not have completeness as a requirement, have you considered just listening to the ~1% statuses/sample stream and collecting tweets that have a specific value for the “source” field?