Two Stage Approach for Multiword Tags
You could pool all the tweets into a single larger document and then extract the n most interesting collocations from the whole collection of tweets. You could then go back and tag each tweet with the collocations that occur in it. Using this approach, n would be the total number of multiword tags that would be generated for the whole dataset.
For the first stage, you could use the NLTK code posted here. The second stage could be accomplished with just a simple for loop over all the tweets. However, if speed is a concern, you could use pylucene to quickly find the tweets that contain each collocation.
Tweet Level PMI for Single Word Tags
As also suggested here, For single word tags, you could calculate the point-wise mutual information of each individual word and the tweet itself, i.e.
PMI(term, tweet) = log [ P(term, tweet) / (P(term)*P(tweet))
Again, this will roughly tell you how much less (or more) surprised you are to come across the term in the specific document as appose to coming across it in the larger collection. You could then tag the tweet with a few terms that have the highest PMI
with the tweet.
General Changes for Tweets
Some changes you might want to make when tagging with tweets include:
Only use a word or collocation as a tag for a tweet, if it occurs within a certain number or percentage of other tweets. Otherwise, PMI will tend to tag tweets with odd terms that occur in just one tweet but that are not seen anywhere else, e.g. misspellings and keyboard noise like #@$#@$%!.
Scale the number of tags used with the length of each tweet. You might be able to extract 2 or 3 interesting tags for longer tweets. But, for a shorter 2 word tweet, you probably don't want to use every single word and collocation to tag it. It's probably worth experimenting with different cut-offs for how many tags you want to extract given the tweet length.