Especially without being in that state, it’d be difficult to guess the political dynamics of a probable proposal in the Connecticut legislature:

On Election Day, voters in 11 states approved constitutional bans on gay marriage. But when the Connecticut legislature meets in January, the state may buck the national trend.
Democrats hold strong majorities in both houses of the legislature. The party’s leaders favor some sort of civil unions which would grant same-sex couples many of the same rights as married heterosexual couples.
Rep. Robert Godfrey, D-Danbury, and other lawmakers say it is almost inevitable that a gay union measure will become law in the 2005 session of General Assembly. …
… The judicial branch is not forcing the hand of Connecticut’s legislature.
At least not yet.
However, earlier this year, seven same-sex couples filed suit to force Connecticut to legalize gay marriage. Some preliminary hearings have been held on the case, which is pending in New Haven Superior Court. The case is expected to take at least two years to decide; most observers expect it to end up before the state Supreme Court.

From now until one side or the other wins at the national level (or both sides admit stalemate, which isn’t likely), every governing body in the country is going to face a variety of concerns: the separate powers of the branches, events in other states, struggles at the federal level, and (oh yeah) constituents’ wishes. Gay rights activists are going to continue with their through-the-courtroom strategy. The mainstream media everywhere, but particularly in the Northeast, is going to accelerate its advocacy. Supporters of traditional marriage will continue to argue that the issue is going to change the Constitution one way or another.
Various states will respond to the forces in different ways, and the federal debate will be shaped accordingly. We can only wait and see what happens, but I’d guess we’ll be seeing it happen in Rhode Island relatively soon.