Congressional votes come first. If it doesn't make it through the Senate, it doesn't get to the states. (But now that Frist has come out for it, Anti-Guv is probably right that the Democrats will have to openly oppose it to stop it in the Senate. If they do, then it becomes an issue in 2004.)
That would be political suicide. A lot of Dems will brank ranks if their leadership comes out against marriage.
There's a reason why Bill Clinton signed the Defense of Marriage Act. He was a scumbag, but no dummy. If the Dems make this an issue in 2004, they will be crushed.