It also could trigger a Constitutional Convention so that a Defense of Marriage Amendment can be considered that would leave the issue of Marriage to each State.
Most likely this would only enrage those who are opposed to same-sex marriage, leading to a huge movement to ban same-sex marriage with a Constitutional amendment. Most Americans do not believe in federalism, anymore. It's either same-sex marriage should be banned on a federal level, or should be legalized on a federal level. Ask anybody on the street what the Tenth Amendment is and they probably wouldn't know.
Such an amendment clarifying that same-sex marriage should be left to the states would be great. It will never happen, though. Not with all the hacks in Washington who think that their views are 100% the best for Murica, and should therefor be shoved down everyone's throats.
It's not that I think those opposed to same-sex marriage are proponents of federalism, but that I think they'll realize that they can't hope to get thirty-eight States to approve an amendment for an outright ban, but by reframing it as an issue to be left to the States, it might be able to pass. Even then it's doubtful it would pass unless it was sent to State Conventions, which the GOP might do if they are in charge of Congress at the time.