Let's talk about RNA since it's simpler and came before DNA.
It's rather simple: RNA can exist; that much is obvious.
Further, nature can spontaneously create RNA that can self-replicate; that has also been shown to be true.
With that in mind it's pretty foolish to think that RNA is the product of an intelligence; it's far more likely that nature spontaneously created it and it got caught up in an oil membrane along with a few other key components, or it formed inside the soup of a membrane that had already formed. Considering it's a fairly 'easy' chemical reaction, and that it had about a billion years to occur in over and over again all around the earth, I don't think resorting to an intelligent designer is called for.
The origin of life is a question not of the ability of RNA to spontaneously form or replicate, but of how all the components of a cell joined together to form the first proto-cell; something that could produce something of at least equal complexity to itself.
What's been proven possible:
1) spontaneous formation of lipid/oil membranes in various different, often unrelated ways.
2) spontaneous formation of nucleic acid polymers
3) spontaneous self-replication of nucleic acid polymers
4) various other things less exciting but necessary
5) for all the different components of life to be present together in one place and for long enough not to degrade too quickly (one theory I like is the rock sheet one - some rock formations form oily organic sheets between their layers; they're safe, protected and have all the necessary ingredients for life)
In reality it's probably a mix of genes-first and metabolism-first; they're not mutually exclusive and one without the other is harder.
http://en.wikipedia.org/wiki/Iron-sulfur_world_theory
http://en.wikipedia.org/wiki/RNA_world_hypothesis