In a poll released by UC's Institute for Policy Research, 46% of Ohioan's "Strongly Oppose" legalizing same-sex marriage. It goes on to say that 11% "Somewhat Oppose," 18% "Favor Somewhat," and 21% "Strongly Favor."
Those numbers aren't terrible, IMHO, for Ohio as a whole. My guess is that, if you polled the urban areas, the numbers would shift in our favor. And 39% in favor... with 11% more swayable, and 3% unsure... well, I think that shows a teachable distinction, yea?
Other findings include a majority in favor of gambling and medical marijuana.
As far as I know, this the only recent poll on the issue since Issue 1 in 2004.