I think this is a diffcult problem to come up with a general policy decision on, because it has many depths.
For one thing, there are the rather basic questions, where there's a simple explanation you know to be objectively true, but you can't find any papers on it because it's been unquestioned truth for a century, OP might just not know his physics (say) well enough. For these things, I think we'll need to accept a leisurely "explain this and move on" attitude; the community shall surely be inhibited by anything else.
Other than that, there are so many levels of quality when it comes to research. If you set a rule where accepted answers must cite a peer-reviewed research, you may think you're doing so in order to establish a definite quality marker, but that is in fact a very arbitrary line on a quality gradient.
There will be good answers out there that will not be able to cite the necessary research. In the soft sciences particularly, you'll find a lot of things are exceedingly difficult to quantify. At the other end of the spectrum, in the hard sciences, you'll find a lot of published papers that simply aren't very good.
I have a feeling that any definite policy here, though well intended, will be to the detriment of the entire community, because the world simply isn't black and white, and you can't draw a line between good and bad answers on the basis of references. Surely, if there are contradicting answers, the one with the most reliable references should in the end be the most upvoted and eventually accepted answer.
I think the process of voting, and of being able to contribute to an old question at any time, and to change which answer is accepted at any time, will prove to be a more flexible and reliable measurement of quality at the end of the day, and if an answer suffers from its lack of references, that will surely be reflected in the number of upvotes it receives.