You can set the Magento search in admin>system>configuration>catalog>search to min of 3 characters. However you’ll probably find that after changing this setting you still get NO results for a 3 letter word.
You’ll probably also need to change the mySQL full text word length variable ft_min_word_len. By default this value is 4, resulting in 3 character words not being indexed.
To change the full text word length variable to 3 add this to your my.cnf:
# service mysqld restart
Finally reindex the magento catalog, you can do this via GUI or command line.
$ php magento/shell/indexer.php reindexall
After the reindex completes you should be able to search your magento store succesfully with 3 character search terms.