"I think it shows there are a lot of delegates, both Democrats and Republicans, that are far out of the mainstream on this issue," he said.
"I hope that, for many of those delegates who support it but are scared that they're doing something that their constituents won't approve of, will begin to understand their constituents actually support it."
Casey Willits, executive director for Fairness West Virginia, said the poll results show increasing support for antidiscrimination legislation.
A 2010 poll commissioned by Fairness showed 61 percent of state voters supported antidiscrimination measures.
"I think our chances get better every single year because the support increases every single year," he said.
The poll also surveyed voters' views on gay marriage.
While 70 percent said they do not believe same-sex marriage should be allowed in West Virginia, about half of voters support some kind of legal recognition for gay couples.
Twenty percent of respondents said gay couples should be allowed to legally marry, while 29 percent said they should be allowed to form civil unions.
Forty-eight percent believe there should be no legal recognition of gay relationships, while 4 percent are not sure.