The Obey seems to be the river of choice when the Caney and Elk have been blown out, for me anyway. We fished it just after Christmas and had good luck with a respectable number brookies and rainbows. We caught most of our fish on #12 BHPT's and some on #18 zebra midges. We also had a few hits on #20 thread midges under a dry, but the hot fly for us has been a big BHPT. Reading Tentwing's post above I don't think you could go wrong with a two fly rig a BHPT above a midge.
Click on the link below, then Fishing Report and there is a report from the Obey down the list a little ways.