Only a small handful of tories support same-sex marriage.
I'm sorry, given the propensity to get confused, I'd ask that you denote which nation's Conservatives you refer to when you do.
Assuming you mean the British Conservative Party, I'd say that the Conservative front bench voted for the Civil Unions bill last year, along with a number of backbenchers. Lets be honest: Civil Unions are gay marriage in all but name; Other than a slight problem regarding pensions, which was actually an oversight on the part of Parliament, they entail identical rights and privileges.
There's also some legal concern over formally calling in marriage in the UK because there is a danger that the state church, the Church of England, may be forced to hand out marriages to gay couples against its will. Given that I don't want to force that sort of situation upon any religious organisation, I'll happily accept the comprimise.