Basically your twitter username/password won't suffice in order to post automatic updates, twitter api requires some more steps described below. No worries, it's rather a simple procedure.
In order to post updates through the twitter API you'll need first to create your own twitter App here: https://apps.twitter.com/
Please provide the 'Callback URL' as well, if you want to interactively authorize your account.
Ex: http://yourblogurl.com/callback is fine, it's just a placeholder. Never used but mandatory for interactive authorizations.
Once you've created your twitter app you have to change its access level to be Read and Write.
Browse to Details tab and click on 'modify app permissions'.
Check the Access level to be Read and Write.
Save your new settings.
Once this is done go to the API Keys tab, at the bottom you should have a button 'Create my access token'.
This step isn't mandatory because you can authorize your twitter account interactively.
It's up to you, if you have only one twitter account that you want to use generate these tokens here.
If you want to use multiple twitter accounts with a single twitter App, then you can skip this step and authorize all your accounts interactively from within the plugin's settings page.
This is it, on the API Keys tab you have all you need, i.e. API (formerly consumer) key/secret, access token and access token secret. If you don't see immediately the access token at the bottom, please refresh the details tab page.