I couldn't find how to do this through the API documentation.
There is an undocumented way to get this information if you're authenticated.
https://api.twitter.com/i/statuses/[tweet.id]/activity/summary.json
An even larger list of API endpoints that are undocumented can be found in the Ruby Twitter library https://github.com/sferik/twitter/blob/master/lib/twitter/client.rb
The New API V1.1 Now supports the tweet favorite's count. Here try it out
stdClass Object
        (
            [created_at] => Thu Apr 04 20:09:16 +0000 2013
            [id] => 319904523520983041
            [id_str] => 319904523520983041
            [text] => North Koreas perspective of the world in the next 5 years http://t.co/MxRgD00VCY
            [source] => web
            [truncated] => 
            [in_reply_to_status_id] => 
            [in_reply_to_status_id_str] => 
            [in_reply_to_user_id] => 
            [in_reply_to_user_id_str] => 
            [in_reply_to_screen_name] => 
            [geo] => 
            [coordinates] => 
            [place] => 
            [contributors] => 
            [retweet_count] => 7
            [favorite_count] => 7
            [entities] => stdClass Object
                (
                    [hashtags] => Array
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