This is an endemic problem with opinion polls. Another set of polls asking about a "public option" and a "government option." The support for the "government option" tanked several points even though it's the same question. There was a rather disturbing GOP poll that mentioned that the democrats "could use (this data) to deny services to registered republicans," and asked "whether this possibility concerned you." It was later retracted as being "inartfully worded"
Another fun poll. Support for taxes helping the poor get insurance was well supported. An easy majority... until you mentioned a number. "Would you pay $500 more per year in taxes to ensure that..." and suddenly we're down to 40%.
I remember a few years back I got a call from some pollster asking about my cable company, and whether I "really thought it was fair that ...." I stopped her halfway through and pointed out that her polls were geared to obtain a specific response, and told her to call me back when she had a neutral poll. Never got called again :P
Part of the problem is that polls aren't nuanced. It's usually "yes/no" or "strongly agree/agree/disagree/strongly disagree." Even asking "would you support a public option" isn't properly clarified. There have been several proposed versions. Some "strong," some "weak," and some downright useless. (the CBO estimated the enrollments for one of the options at ZERO) Which one are you asking about can be important, but if you ask "Do you support the public option proposed in HR-3200's pre-amended writing," most people would answer "Huh?"
If literally changing the name of the subject can push support above or below the majority line, you know the public is not properly educated on the subject. That will always be exploited.
I'm glad I'm not a senator. I'd be hard pressed the balance the desires of the people with the fact that sometimes you can't tell what it is they actually want!