Statistics guru Nate Silver reports the poll numbers:
The most recent poll was conducted by Civitas Institute, a conservative think tank whose poll results have generally shown little partisan bias in the past. That survey polled Democratic and Republican primary voters separately, but projected that the measure would win by 16 percentage points when it combined the results. An April poll by Public Policy Polling, which conducts polling for Democratic clients but whose surveys also have a track record of nonpartisanship, had the measure prevailing by 14 points.
Silver points out that support for the ban nosedives when voters understand that it also outlaws civil unions. Our side has failed miserably in making that point very clear.