I don't think it's a conflict with the social widgets, but i could be a conflict with one of your plugins or the theme itself.
What is more likely is that your server cannot connect to the Twitter API because the rate limit has been exhausted.
A future version of the plugin will have a debugging option that will help diagnose these kinds of issues.
If you know how, ssh on to your server and type
curl http://api.twitter.com/1/account/rate_limit_status.xml. This will return something like:
If your remaining hits value is zero, you know that the rate limit is the issue. This may not be your fault. If you are on a shared server someone's site may be responsible.