I don’t think that the publish-action in your twitter plugin is your problem. You probably have a twitter widget or something similar, which will display your twitter posts/status on your blog page.
Twitter access his API with a javascript library. Look in your sourcecode. In the HTML HEAD Element, you should see a call to the twitter platform url:
<script type="text/javascript" src="http://platform.twitter.com/anywhere.js?id=&v=1&ver=1"></script>
This call from your site to the twitter api isn’t encrypted. Your browser will show you a message, which will tell that your content is only partial encrypted. The SSL lock isn’t displayed.
I’ve tried to call the platform.twitter.com url over HTTPS. But the certificate is only valid for twiter.com.