You may or may not be aware that Twitter have stopped third party applications from using Basic Authentication. For those who are not quite clear on the mechanics of authentication, when using Basic Authentication you (or your program) send a Username and Password with each request.
This documentation details how to allow one instance of tcli (OAuth) to be used for multiple user accounts,
mod_BTwitter is a simple module designed to embed a users timeline into Joomla based sites. At the core of it's design is the principle that there should be no un-necessary chrome and page load speed should not be adversely affected.
This documentation details how to use mod_BTwitter