Several pundits on the right and left believe overturning Roe v Wade would prove politically disastrous for Republicans, principally by mobilizing a great army of heretofore silent pro-choicers and secondarily by demotivating pro-life conservatives. Ramesh Ponnuru argues that this view is completely wrong because the public is not nearly so pro-choice as the left wishes. He theorizes in a related article that Roe enjoys majority support only because the public misapprehends the breadth of the ruling.
Ponnuru doesn't offer any data to quantify the size of this ignorance distortion, but I recently stumbled across a rarely asked poll question that starkly illuminates the scope of public confusion. This 2005 Harris poll asks "In general, do you think that abortion should be legal or illegal during the following stages of pregnancy?" Respondents could answer "legal" or "illegal" for each trimester of preganancy, described as "the first three months of pregnancy", "the second three months of pregnancy", and "the third three months of preganancy". A full 86 percent of those polled said abortion should be illegal in the third trimester of pregnancy, while 72 and 38 percent said abortion should be illegal in the second and first trimesters, respectively.
In the same poll, 52 percent of respondents favored Roe (the poll explains that Roe overturned state laws outlawing abortions in the first three months of pregancy). Juxtaposing this number with the 86 percent who would make abortion "generally illegal" in the third trimester shows that 73 percent of those who support Roe (38 of the 52 percent) would make third-trimester abortions illegal. These folks don't understand that the inextricably linked rulings of Roe and Doe v Bolton effectively eliminated all abortion restrictions through the ninth month of pregancy. (To calculate that number I'm simply extracting the overlap of the 86 and 52 percent--or those who selected two mutually exclusive answers: 86 + 52 - 100 = 38)
A similiar comparison shows how flexibly some label themselves "pro-choice". Fifty-one percent of respondents identified themselves as pro-choice while 44 percent called themselves pro-life. Thus over 72 percent of self-identified pro-choice respondents would outlaw third-trimester abortions (37 of the 51 percent) and 45 percent would also ban second-trimester abortions (23 of the 51 percent). On the flip side, just nine percent of pro-lifers would allow even first-trimester abortions (4 of the 44 percent). (Again this is calculated by overlapping the 60 percent of respondents who prefer abortion to be "generally legal" in the first trimester with the 44 percent who call themselves pro-life.)
UPDATE: James Taranto reports a fortuitously timed poll that roughly corresponds with my conclusions. The poll asked respondents to choose which of three answers best decribes the impact of Roe on abortion law. Seventy-one percent chose an incorrect answer or said they didn't know--almost exactly same percentage of Roe supporters I said misunderstood the ruling's impact in the 2005 Harris abortion poll. Note that the 71 percent who misunderstood Roe in this new poll were from the entire population of respondents, not just Roe supporters. However, it's not unreasonable to assume similar numbers of Roe opponents also underestimate the breadth of the ruling, and simply oppose abortion in nearly all circumstances. That fits well with my other conclusion that a very small percentage of pro-lifers would allow even first-trimester abortions.