Does legal abortion have deep roots?

Even though I'm no fan of Michael Kinsley, I think he makes an interesting point in his recent column.

He writes,

"Others emphasize that social policies can start with a Supreme Court ruling and develop into deeply rooted national values. That happened with Roe and abortion, they would say, while the opposite happened with Bowers and laws against homosexuality. Of course, if a policy really has become a deeply rooted national value, then the once-controversial Supreme Court ruling is superfluous, because democracy will protect such a value. The fear that motivates the Roe panic is that the rights at stake are not deeply rooted. Or not deeply enough."

If Roe and legal abortion are so deeply ingrained in our conscience as a nation, then why are pro-choice organizations so scared about having the issue returned to the democratic arena? If the large majority of Americans are pro-choice, then why not give them a chance to have their voices heard by voting for pro-choice candidate who would protect legal abortion?