Of course Obama is for gay marriage. They have been solidly behind him. He owes them and he pretty much said that.
Otherwise, no, gays do not have any inherent right to get married. That right should be granted to them by the general population. If the population of say a state do not wish to grant them this right, then they should not be able to get married. This is not an individual's right. It is a social matter.
Marriage is a social matter; this is why it is a publicly declared contract. Otherwise, two people can live together and have sex with each other, cheat or not cheat on each other all they want. Why make it a social matter?
The idea, that has been utterly lost, is that this is one of very few areas where individual's right has huge interaction with that of the society. No society can survive without getting new members. New members are predominantly through children. Children must be cared for and trained. A society has to decide how this is done. You can for example, as many would like but are too coward to explicitly say so, create new children then give them to social institutions to be trained the "right way," essentially what Hitler liked and many other socialist like.
Marriage is about this issue. It says that a family unit is formed and publicly declared, the contract is not just between the individuals, but between the individuals and the society, and then the unit is entrusted with raising children and the society will support them for the valuable service they are providing. This is called marriage. This is why a breach of this contract, i.e. cheating, is society's business. Otherwise, why should the society get involved if a man decide's to cheat on his wife. Whose business is it anyway? What right do I have to get forcefully involved if a man breaks a woman's heart?
People instinctively know this but have in general lost the higher order understanding of it, so they make incorrect abstract arguments that are inconsistent with how they instinctively are behaving.
Now you have to decide on what the family unit is. Society grants this status. It is not an individual matter.
As far as the argument that one is born gay or not, it is the same as with anything else. Similarly a person is born with a propensity to steal, cheat, or lie, but that does not necessarily make stealing, cheating or lying a good thing. One decides on those based on other criteria than the fact that the person was born with a propensity to steal, cheat or lie.