Reportedly thirty-three states have now begun considering bills to promote or require the revolutionary HPV vaccine (here's a summary of six of those). While cultural-conservative response during the FDA approval process was relatively muted (as compared to the long struggle over OTC emergency contraception), there is now a full-blown debate about whether the vaccine should be mandated, largely arising from HPV's status as a sexually transmitted disease.
Inevitably, the litigation has begun, with several Texas parents challenging Texas Gov. Rick Perry's executive order mandating the vaccine for sixth-grade enrollment. While the claim in this case appears to one in state law alleging that the Governor exceeded his authority, this will not be the only such suit, and others will surely raised constitutional objections. These claims, I expect, will be based either on the right to bodily integrity or the right to direct the upbringing of one's children. Free exercise claims are also imaginable, although the mandatory vaccination bills out there seem generally to include religious exemptions.
The natural question becomes the application of Jacobson v. Commonwealth, in which the Supreme Court in 1905 rejected a constitutional challenge to mandatory smallpox vaccination. The Court there held that (1) individual liberty interests could in appropriate circumstances be overridden by public health measures, and (2) the legislature having judged a mandatory scheme proper in accordance with overwhelming medical opinion, it was not for the courts to undertake a fresh examination of claims about the safety or efficacy of the vaccine. That case is still good law, as demonstrated by the Court's need to distinguish it in the Cruzan case, and by a military appeals court's recent reliance on it to uphold a mandatory anthrax vaccination. U.S. v. Schwartz, 61 M.J. 567 (N.M. Ct. Crim. App. 2005).
Of course, one vaccination is not the same as another; the public health implications of cervical cancer and smallpox are also quite different. Nearly 12,000 diagnoses and 4,000 deaths per year is a serious problem, but it is not highly contagious and does not rise to the level of a public emergency.
On the other hand, the potential parental objections seem relatively slight. Rather than asserting that the HPV vaccine is dangerous (as in Jacobson), parents would presumably be asserting simply that its safety and efficacy are uncertain, and/or that it would interfere with their parental prerogative in teaching proper sexual values. As in Jacobson, medical authority overwhelmingly supports the safety and efficacy of the vaccine. The risk of physical harm is merely speculative, as is the "risk" that vaccination would encourage adolescent sex. In any event, vaccination in no way prevents parents from teaching their children - and if they want to teach them to fear sex, there are plenty of other risks to spook them with.
Nevertheless, I would expect to see some ingenious arguments being made against mandatory vaccination, in both the legislatures and the courts, as this issue plays out across the country.
Edit: As the commenter below rightly indicates, the forthcoming legislation will likely have generous opt-out provisions, thus largely vitiating any constitutional objections by parents. In the context of school prayer, the Supreme Court has said that opt-outs are not enough to protect the objector because the opting-out child may be ridiculed by others. No such concerns apply here, and even if they did they only really have force in the Establishment Clause context. I shouldn't be surprised, however, if some creative arguments are put out there to challenge vaccination nonetheless -- so much is suggested by the current political debate, despite the opt-outs.