There are two arguments I would make against the claim that "we can't allow this or it will lead to that."
Point One: we use the law to draw specific lines all the time.
That's what it's for.
Point Two: warnings about the risks of redefining marriage present gay marriage as though it exists along a continuum with polygamy, incest and bestiality.
About Point One
It is not the case that drawing the line beyond "one man and one woman" will mean we must draw it again elsewhere.
Think about the laws that govern the freedom of religious expression vs. the freedom from religious imposition. It is precisely in the courts and the legislature that we monitor the pendulum swings society takes around this issue. Despite all the Sturm und Drang about it (including on my part!), I think we do pretty well.
Similarly, we will always have to attend to where to draw the line on civil liberties like the bearing of arms, and freedom of speech. We will always be working to find consensus in these areas - stasis is unlikely. Maybe that's a good thing: the push and pull keeps us in the middle.
It is a naive argument then, to say "if we allow this, pretty soon we have to allow that." If we allow people to gather on the National Mall to demonstrate about unfair taxation or reproductive rights, eventually we will have to allow people to let themselves into your home and shout you down about their beliefs? Of course not. Allowing 16 yr-olds to drive will lead to allowing 14 yr-olds to drive? No. In fact, most of our laws are vulnerable to the slippery slope argument. How much information should intelligence agencies have to provide? When is self-defense an appropriate claim? What accommodations for the disabled should employers have to make?
We use the courts and the legislature to draw lines - it's how we operate. People who support gay marriage are asking to have the line moved from including only heterosexual couples to including same-sex couples. We aren't asking for the county magistrate to ratify the union of a man and his horse.
About Point Two
The various types of unions warned against by people against gay marriage can't all be lumped together.
Hopefully it's just rhetorical flourish when conservative politicians predict that the demand to marry a sheep or a motorcycle is the logical conclusion of the effort to expand the definition of marriage. I'm not even certain how to address that one - it tempts me to fall back on an appeal to common sense. I try not to do that, because as a nation, if we could agree on what is "common sense" we wouldn't be in this predicament now. But to paraphrase Jon Stewart, "Does your wife know you can't tell the difference between a beloved, life-long companion and a favorite turtle?" I'll just say that when a person is seriously attracted to an inanimate object or an animal, the American Psychiatric Association calls it paraphilia, and recommends treatment. They came to their senses and stopped including homosexuality in that category four decades ago, so let's try to separate those ideas now.
Pedophilia can be removed from that list of concerns as well. It too is considered a psychiatric disorder, it is a crime, and the issues of harm and consent disqualify it from even being considered in the same discussion as the one about marriage equality. The latter is about problematic laws against the marriage of two consenting adults, who would be legally be eligible to marry someone of a different sex, but are not allowed to marry each other. The former is about sexual predation.
As far as incest, comparisons have been made with some humor about the greater legal acceptance in the US of marriage between first cousins vs. marriage between same-sex couples. I honestly know very little about the arguments for and against cousins marrying. I would just say that concerns that marriage between cousins is waiting on the slippery slope below gay marriage aren't valid, since it is already legal in many states.
Regarding polygamy, this is the one question along these lines that I think is legitimate to raise. While it is still a very different animal from same-sex marriage, which is a basic right that is currently being denied, the question of polygamy is most closely related because it is an arrangement that has been widely accepted in some realms, and is not necessarily an expression of individual dysfunction.
Monogamy is a purely social construct, without any grounding in biological necessity or psychological health. It is a decision a culture makes about how it wants to organize families. I personally am miles away from even taking the time to sort out the pros and cons of legalizing polygamy. I don't think it's a priority, and because it has historically been so patriarchal, I acknowledge a distrust of the idea. But at least here, we have a reasonable question: if we expand the definition of marriage from one consenting adult male and one consenting adult female to include consenting adult same-sex unions, why not three of the above?
This question then returns us neatly to Point One. Legalizing one does not mean legalizing the other. If an appreciable national movement to legalize polygamy were to form, it would have to take the same path as we are taking to legalize same-sex marriage. Obviously, it is an arduous path. They would have a long way to go to make their case. And most importantly, the case for gay marriage would have nothing to do with it. Gay Americans are asking for their constitutional rights to equal protection and privacy. If people supporting polygamous unions intend to stake the same claim, their challenge to the law, like every other, will be taken on it's on merits, unrelated to challenge being made in the name of same-sex marriage now.