Hello,

I am using the default template in LimeSurvey 2.7.3 and would like to be able to share a user's answer for every question on Facebook and possibly Twitter.

Is this an option? how would I do this? Is there a plugin for this?

There is no feature or plugin (at least it was never mentioned or shown here in the forum) to support publishing answers to facebook.

The feature you're looking for is available in some bigger surveytools.
E.g. Qualtrics with actions modules:
www.qualtrics.com/support/survey-platfor.../setting-up-actions/

Personally I would never post a survey question automatically via a twitter or facebook account I own.
Sounds like begging for trouble.