2 routes toward persuading the skeptical about gay marriage: pathos or pocketbook
Take your pick. One method works it's magic on the heart-strings all by itself...From The Nation:

For centuries, from ancient Roman comedy to My Big Fat Greek Wedding, lovers have been overcoming recalcitrant parents and progressing toward the triumph of a marital finale. Gay men and lesbians seeking to tie the knot in one stubborn county after another re-enact this familiar wedding plot again and again. In turn, the state, blustering about the end of civilization like the swaggering capitano of the commedia dell'arte, plays the villainous authority who thwarts the inamorati. The public is well practiced in whom to root for. At a time when tabloid headlines and reality TV shows make a nightly travesty of eternal devotion and connubial bliss, queer sweethearts have provided the season's most sincere and sentimental romantic comedy.

The other reaches for the purse-strings...
via Kos:

Allowing same-sex couples to marry would have a positive impact on the federal budget, according to a report from the Congressional Budget Office on Tuesday. Same-sex marriage would boost federal income tax revenues by $400 million per year until the end of this decade, mainly because of the so-called marriage penalty, the office said. While Social Security payments would rise over time, as would spending on spousal health insurance benefits for federal workers, other expenditure items would be much lower, since spending on Medicaid and Supplemental Security Income would fall. The net impact would be a federal budget savings of nearly $1 billion per year.

I hadn't really thought of either before. Whatever works...