The State House News' latest poll has the 2008 DoMA ballot initiative here losing if folks voted now. Results from 400 registered votes were 51.9% to 42.6% opposed to the ban.
That is not an insurmountable lead, but the trend in various polls has been for slowly building support for same-sex marriage. It certainly appears that the hysteria that repeal folks tried to generate over terrible things and even chaos resulting from such unions has backfired. The longer voters see zero change from expanding marriage, the less likely they are to want to take away this right.
As is the wont of pollsters, Gerry Chervinsky of SHN was cautions, noting that the poll had a plus-or-minus for error of 5%. He also predicted a bitter fight over the proposed amendment.
Plus, he hesitated to predict the eventual outcome. "(T)hese ballot questions are hard to poll. It's the world of the hidden vote, where people want to tell you the politically correct thing. But when they get into the voting booth and pull the shades, they go - 'hmmm, maybe I won't vote the way they think I should.'"