The movement in question clearly has a significant degree of influence on the grassroots politics, as demonstrated by the outcome of the 2008 election. Being able to call upon a sizable membership will most certainly help the Sanders campaign gather more steam as we head in to the crucial period leading up to the elections.
While a somewhat recent political organization, MoveOn.org is becoming a political heavyweight and its endorsement of any candidate is likely to have an effect on the race. While perhaps not being a definitive decider of any given election, it has enough credibility to tighten things up, or make a not so close race a bit closer.
Generally speaking, the regular public only reads headlines and then forgets the story about a week or two later. The mainstream elite establishment is counting on this collective distraction to advance their agendas. Bernie Sanders is completely reliant on the notion of taking wealth from earners and giving it to non-producing voters.
I don't think that people look at stuff like that when they decide on who to vote for anymore. It almost all comes down to stupid things like personal scandals or lack thereof. Most people do not do any research or really listen to the issues on the available candidates anymore.