The theory behind trying to pass such an amendment takes into account the contemporary erosion of state's rights and voter's rights by the ACLU and the activist courts, which have been seeking to rule from the bench for 40 years and largely succeeding. Even though states have held referenda on the definition of marriage and overwhelmingly voted to retain the one-man-one-woman standard, a single Federal judge can and has struck down state referenda, the DOMA (federal Defense of Marriage Act) notwithstanding.
The theory is that the proposed amendment would have to circulate in all state legislatures over a three-year period in order to be ratified, which would force each state to confront and debate the question legislatively.
There has been hopeful movement in the direction of quashing judicial overreaching in the decision this week by the Maryland Supreme Court, which overturned an activist judge's attempt to hand down same-sex marriage from the bench. The opinion did not boil down to favoritism towards a definition of marriage, but noted that this question should not be determined by the judicial branch, but rather by the legislature.
It was not a clear-cut victory for the one-man-one-woman camp; but it was a hopeful step in placing the question before the representatives of the People.
Yet Congress can choose to exempt pretty much anything from Federal courts' authority if they want to, certainly more easily than getting an amendment ratified. And if leftist judges cannot read the plain wording of the existing laws & Constitution, then why should we expect they'll respect the wording of a new amendment?