A WordPress Plugin which Tweets the new posts with its title, link, Author's twitter handle and a featured image from the post.
You will find a menu called Tweet My Post under Users. Open it and set your Twitter Handle.
You will find the instructions under Tweet My Post menu.
You can check the reason at TMP - Log page. Most probably because you have not set your API and Access Tokens/Secret. Another well-known cause is, your Twitter app has only read permission. Update setting to read+write permission and re-create access tokens.