Now, back in September 2005, the Constitutional Convention shot down a similar amendment - but that one was proposed by a legislator, and thus needed majority support to pass. This one still needs to make it through a second Constitutional Convention in the 2007-2008 Legislature; if it does, then it goes on the ballot. (If I read Article 48 of the Massachusetts Constitution correctly, it could go on either the 2008 or 2010 ballot, depending on when the Constitutional Convention acts on it.)
The proposed amendment is, IMNSHO, a remarkably dumb idea. There are, however, a couple of potential upside to this process. For one thing, the Legislature can shoot this down pretty much anytime the leadership can muster the votes - and I wouldn't be terribly surprised to see a Constitutional Convention in mid-August or thereabouts.
The other possible upside is that there isn't any huge popular uproar against gay marriage here in Massachusetts. It's been legal here for over two years (the first marriages were performed May 17, 2004 - the fiftieth anniversary of Brown v Board of Education), and the world has conspicuously failed to come to an end. If this amendment does make it on the ballot, I expect an ugly fight, but I can see it losing badly. A lot of folks in this state know one or more same-gender couples (several of which attend my own church). So there's at least a decent chance that, if things come to a vote, the voters of the Commonwealth will reject this amendment. Which might be the best of all possible outcomes.