I am going to wade into a conversation that occurred about a year ago but which was rekindled recently by an article in Slate that asked the question: "Where is the Great Mormon Novel?" The article was written as a critique of the new novel by Mormon Brady Udall called The Lonely Polygamist.
This article lead back to an article in the Mormon Times that stated that the Great Mormon Novel is impossible for impossibly shallow reasons thoroughly discredited here and here. The gist was that Mormons are not self-critical enough and not willing to question beliefs enough to write great literature. The discussion then turned a bit more meta with the proposition that we shouldn't even be worried about creating the Great Mormon Novel because the concept itself is outdated and unworthy of our attention. This is my incredibly glib recap of the discussion and I encourage you to read through those links and flesh out the arguments for yourselves. (As a side note, if you haven't spent some time exploring Mormon artistic endeavors at A Motley Vision and Dialogue, it is worth your time to do so.)
I think transcendent literature is something that is universal to our shared human experience. What makes a piece of literature timeless is that it speaks to people from different backgrounds, cultures, eras, and genders, and can reveal something new to each. My initial reaction, then, was that a Great Mormon Novel is not very likely, not because we aren't able or willing to question faith and authority and embrace ambiguity and conflict, but because we are pretty weird. Pres. Hinckley, on several occasions, reiterated the words of the apostle Peter in referring to us as a "peculiar people." We have always been encouraged to live apart from the world and embrace our peculiarity.
Of course the Gospel is universal, but a piece of Mormon literature is not just a rephrasing of the Gospel. Mormon literature is about Mormon culture and the internal and external difficulties we face in our quest for faith, individualism, collectivism, and understanding. There really has never been anything remotely like Mormonism and the culture we've created, I think, and therefore trying to connect it to a wider audience through literature might be a task that cannot be perfectly accomplished (which would, in my mind, be the definition of "Great").
I'm not implying that there is not great Mormon literature out there, there certainly is. But a novel by a Mormon about Mormonism that is widely regarded as a masterpiece of literature that crosses boundaries might be too much to ask. We're just too different.
The more I've thought about this, however, the more I think my initial reaction might be wrong and that might be an indication of unhealthy pride more than anything. A Mormon's journey through life is not so much different than other people's. Like everyone we are trying to develop stable relationships, confront our internal and external demons, make sense of contradictions, and find peace in a decidedly unpeaceful world. We're not above any of that, and the ability to illuminate these issues is what makes literature great, and potentially Great, and I think doing so in the context of Mormon beliefs and culture is just as likely as any other culture or point of view.
The lack of the Great Mormon Novel is not an indictment of our literature or beliefs, it's just that there are very few Hemingways, Foster Wallaces, and Jameses and there are really just very, very few Mormons in the world. But it might just be that very uniqueness of point of view that makes a Great Mormon Novel possible. One of the ways that Great literature is able to provide that freshness and universality that people crave and remember is by providing a new point of view that sheds a slightly different light on an otherwise mundane subject (think of the way Elder Bednar is able to talk about subjects we've heard hundreds of times from a new perspective that sheds some new light on it and gives us a deeper understanding).
I recently came across an idea from Mormon writer Karl Keller that I think expresses all of this well. His point was that great Mormon art is "not art filling a religious purpose, but religion succeeding in an aesthetic way." We have this incredibly beautiful and rich religion that can succeed in an aesthetic way, and our literature can reflect that and cross boundaries and be recognized as something Great.
But we, as a religion, really need to do a better job promoting that art. We need to consume it, demand more of it, and think and talk critically about it. We need more than the traditional Deseret Book fodder, which only strives to inspire rather than find true understanding through a confrontation of ambiguity and conflict. There is nothing wrong with inspiration from time to time, but it can't be the principal goal of our art.