From and email he sent to church members:

“For 5,000 years, every culture and every religion – not just Christianity – has defined marriage as a contract between men and women,” Warren wrote. “There is no reason to change the universal, historical definition of marriage to appease 2% of our population.”

He explains his support in this video.
He mentions in the video that both Obama and McCain defined marriage as between a woman and a man when they took part in his debate at Saddleback. Here’s Obama’s full answer:

WARREN: There’s a lot more I’d like to ask on that. We have 15 other questions here. Define marriage.
OBAMA: I believe that marriage is the union between a man and a woman. Now, for me as a Christian — for me — for me as a Christian, it is also a sacred union. God’s in the mix. But –
WARREN: Would you support a Constitutional Amendment with that definition?
OBAMA: No, I would not.
WARREN: Why not?
OBAMA: Because historically — because historically, we have not defined marriage in our constitution. It’s been a matter of state law. That has been our tradition. I mean, let’s break it down. The reason that people think there needs to be a constitutional amendment, some people believe, is because of the concern that — about same-sex marriage. I am not somebody who promotes same-sex marriage, but I do believe in civil unions. I do believe that we should not — that for gay partners to want to visit each other in the hospital for the state to say, you know what, that’s all right, I don’t think in any way inhibits my core beliefs about what marriage are. I think my faith is strong enough and my marriage is strong enough that I can afford those civil rights to others, even if I have a different perspective or different view.

It would appear that Obama wouldn’t have a problem with Prop. 8 since he opposes gay marriage and thinks the states should decide the issue.
Biden appears to support it in the VP debate:

IFILL: The next round of — pardon me, the next round of questions starts with you, Senator Biden. Do you support, as they do in Alaska, granting same-sex benefits to couples?
BIDEN: Absolutely. Do I support granting same-sex benefits? Absolutely positively. Look, in an Obama-Biden administration, there will be absolutely no distinction from a constitutional standpoint or a legal standpoint between a same-sex and a heterosexual couple.
The fact of the matter is that under the Constitution we should be granted — same-sex couples should be able to have visitation rights in the hospitals, joint ownership of property, life insurance policies, et cetera. That’s only fair.
It’s what the Constitution calls for. And so we do support it. We do support making sure that committed couples in a same-sex marriage are guaranteed the same constitutional benefits as it relates to their property rights, their rights of visitation, their rights to insurance, their rights of ownership as heterosexual couples do.
[…]
IFILL: Let’s try to avoid nuance, Senator. Do you support gay marriage?
BIDEN: No. Barack Obama nor I support redefining from a civil side what constitutes marriage. We do not support that. That is basically the decision to be able to be able to be left to faiths and people who practice their faiths the determination what you call it.

But even though he opposes gay marriage, he stated on the Ellen Show that he opposed Prop. 8:

If I lived in California I’d truly vote against Prop. 8 And btw, Barack and I opposed a similar attempt nationally that there was an attempt to talk about a constitutional amendment which I think is regressive, I think is unfair and so I’d vote no on Prop. 8

Here’s the video of the Ellen Show where he made that comment.Clearly he’s flip-flopped but has Obama? Obama believes the states should decide this issue and has stated that he opposes gay marriage, so you’d think that he would be for the citizens of California deciding this issue themselves and that he would support the measure since he believes that marriage is between a man and a woman.
BTW, why in the world didn’t Ellen ask him why he said that he opposed gay marriage during the debate? Seems like a natural question, afraid that her candidate might flub the answer?