This is a great idea, but even though I tell people I am an "Internet consultant", I don't know what you mean by "social media campaign". Can't we just refer to these types of communication as "marketing"? It's a topic people know and about which there is tons of information.
For some reason marketing only seems to be a common idea with larger NPs that are more like corporations. But the concept can benefit just about any NP.
Making phone calls will take more time than most other forms of marketing (search advertising, banner ads, email, direct mail, etc.) but as one of the more personal methods, I have to think it would be more effective both in cost and end results.
The only suggestion I would make for an organization considering this on a large scale, is that they get permission from the people they are going to call at some point. NPs don't have to abide by the national do-not-call list, but they should in my opinion. Most people are on there because they don't want phone solicitations. I have lost interested in several NPs due to abusive phone marketing, and I generally vote against politicians that use the method. :-)