This announcement from the newsroom (related to ENDA and a statement from Harry Reid that “the church is changing” [ftnt1]) contains this sentence: “As such, traditional marriage is a foundational doctrine and cannot change.”
I find the idea that a doctrine cannot change to be more than a little problematic. It seems to me that a commitment to continuing revelation requires one to accept, at least in the abstract, the idea that doctrine could in fact be changed in the future. (That said, I can’t imagine the church permitting gay marriage for church members. I’m just speaking theoretically here.)
And I’d think that a church that had first practiced traditional marriage (whatever that means–see here for a great exploration of how the church’s doctrine concerning traditional marriage has changed just in the last 40 years) and then adopted polygamy and then ceased practicing polygamy–all, presumably, at the behest of revelation–would not claim that the doctrine concerning marriage could not change via revelation.
That said, I think I understand the impetus for saying not only “the church’s position has not changed” but “the church’s position will not change” because I frequently hear in the bloggernacle–whether the topic is gay marriage or anything else the commenter does not like–the sentiment to “just wait” because in a generation, the doctrine/policy will have changed. I can see the appeal of this line of reasoning–it would be bizarre to think that nothing will change in a church that believes in continuing revelation and so it isn’t worth getting too bothered over–but I see the danger in it as well, as we begin to basically ignore doctrines that we don’t like while we wait for them to go away, instead of grappling with gaining a testimony of them instead. So maybe the “cannot change” language is an important signalling device–contra Elder Holland’s “one miracle at a time” comment when he was asked if women would one day be serving missions for two years instead of 18 months–that there are some changes that are not in the works and won’t be happening any time soon.
I suppose I also need to consider the possibility that President Monson has specifically received a revelation that the doctrine concerning gay marriage will never, ever change. I think that that is within the realm of possibility, although I can’t think of many precedents for that kind of a revelation. I would hope that if that were the case, we would hear it from him and not just from the newsroom.
 Reid’s statement, in context (at least, as reported in the two articles I found–I can’t find a complete transcript), appears to say that more members of the church are supporting “gay rights,” not that the Church as an institution is changing its doctrine on gay marriage, which makes the newsroom response seem a little off of the mark, especially given that the institutional Church has itself actually supported “gay rights” in some cases. (But I suppose the newsroom mitigated this criticism to some extent with its conditional statement: “If it is being suggested that the Church’s doctrine on this matter is changing, that is incorrect.”)