Is there a module that saves Twitter posts in a custom table? I need to save Twitter posts in Drupal 7, but I don't want to create a node for each tweet.

Is there a module that can save them in a custom table?

Thanks.
Try the feeds module and data module

http://drupal.org/project/feeds 
http://drupal.org/project/data


and import the rss of your twitter feed or search into the feed than save it as a simple database record with the data module.