https://api.twitter.com/1/statuses/user_timeline.json?include_entities=true&include_rts=true&screen_name={screen_name}&count={count}
it's important to include the line include_entities=true to the request. This will give you an expanded response including re-tweet and mention counts.
Update:
to get tweets from the last 90 days, there is a Node.js library you can use called Snapbird
https://github.com/remy/snapbird
.. and here is another resource covering the same topic.
http://blog.tweetsmarter.com/twitter-search/10-ways-and-20-features-for-searching-old-tweets/
