Did you follow the set up guide in the documentation?http://trinitronic.com/index.php/Downloads/nice-article-tweets-documentation.html
Twitter has very specific Security protocols that have to be followed in order to communicate with their site. Please review the documentation at the above link and ensure that you have entered the "Consumer Key" and the "Consumer Secret" correctly into the extensions settings.
Once you have verified this, let me know if you are still having difficulties. I am happy to work with you towards a satisfactory resolution.
~ All the best