Eugene Volokh (I've been quoting him a lot) recently posted law review article about the mechanisms of the slippery slope and its effect in relation to same-sex marriage (SSM). I've cited his analysis of the slippery slope in the past (here).
In short, he lists two types of slippery slopes and then applies them to two arguments made by opponents of SSM.
1) Attitude Altering
If society legalizes conduct, people who are unsure of its correctness will often defer to the legislatures or courts and presume their legal decisions are synonymous with the conduct's moral veracity.
If SSM is legalized, a greater number of people will support other nontraditional arrangements on the assumption that we must treat similar parties similarly.
He applies these mechanisms to two potent arguments:
A) The law will slope down to polygamous marriages.
1) Allowing SSM will make it more acceptable to make changes in the standard definition of marriage. While today people might be opposed to polygamy, in the future they might see SSM as normal and their attitude will shift to favor polygamy because SSM and polygamy rest on similar principles.
2) Moreover, polygamy will become accepted because SSM is rooted in concepts that apply equally to polygamy. If SSM is justified on the grounds that people can choose to marry whomever they wish, some people will argue that logic applies to polygamy as well.
In the case of both these arguments, Volokh is careful to point out that polygamy and SSM can easily be distinguished but his argument is that many people will not do that.
B) Legalizing SSM will lead to the government proscribing private discrimination on the basis of sexual orientation.
1) Can a tenant advertise for a heterosexual roommate? Today, as far as I know, the laws of no state ban such advertisements But if SSM is legalized, society will come to view homosexuality in a better light. Preferences that might seem rational today (not having a roommate who is attracted to one's gender) would be viewed as motivated by irrational animus. Hence the legitimization of homosexuality could cause a domino effect that would topple private actors' decisions insofar as hiring, rooming, or renting goes.
2) Moreover, the recognition of SSM would likely rest on principles that parallel the civil rights movements. That movement lead to Title VI, which banned employment discrimination and other acts designed to prevent explicit discrimination. Logically, we could conclude that people might view sexual orientation in the same vein: first we disallow bans on SSM, then we prohibit discrimination by employers.
Volokh supports SSM despite these arguments for utility reasons, and does not view SSM with moral disapproval.
The question of SSM is complex. I believe even in the absence of a slippery slope, which as I noted before I do not generally subscribe to, there are moral and social reasons to ban the modification of our long-standing institution. Volokh alludes to a "Burkean" concept: we should not make frivolous changes on the basis of a whim. This idea underpins conservatism, and in my eyes, is a sufficient basis for denying SSM by itself. Volokh's arguments only buttress this reason.