this is a good question. i'm a one-woman show, and it's virtually impossible to keep up with all my social networking/promotion and do my work at the same time.
I feel that it depends on the size of the organization, for example if you were to have several types of twitter accounts (customer service vs. online research) and several facebook pages, the company would need to hire a full time person whereas if it was a smaller company with only one twitter account and facebook page maybe you would only need a person on a part time basis.
I personally am finding that a good deal of time and effort is required to maintain an effective social networking campaign. We started with an intern working full time on this initiative for us, however we quickly realized that it requires more time and definitely a greater level of expertise.
From Tresa: Our strategy has revolved around providing key messages to all of our employees through brand training so that the task does not have to fall on on person. This approach also allows for different areas of the company to provide unique perspectives that are still on-brand, ultimately informing the company of how we are doing internally on brand.
I think if you are serious about building a social media presence, you need at least one part-time person dedicated to managing and building online branding and web presence. Consistent, timely management and interaction with a web community is what helps to build audiences and loyalty. If you are stretched too thin with other responsibilities, it's impossible to manage your social media presence in an effective way...unless you are prepared to work 24/7. It's not just about managing and monitoring the tools, it's also about developing and executing strategy and tactics. Social media is a trial and error process...it takes time to find the right voice and content which encourahes interaction and engagement with and from target constituents.