Co-opt the Health Care Reform bill to restrict abortions?

The House health care reform bill tries to work around the law that forbids taxpayer money going to pay for abortions. Note how that would work, but also note the possibility of a pro-life result that has pro-abortionists nervous:

The House approach to the coverage of the procedure in federally subsidized insurance plans is presented as a compromise: Abortions would be funded out of the premiums that come from individuals, not money from taxpayers. But this is a cover, if not a con. By the nature of health insurance, premiums are not devoted to specific procedures; they support insurance plans. It matters nothing in practice if a premium dollar comes from government or the individual — both enable the same coverage. If the federal government directly funds an insurance plan that includes elective abortion, it cannot claim it is not paying for elective abortions. . . .

The House bill would result in federal funding for abortion on an unprecedented scale. But forbidding federal funds to private insurers that currently cover elective abortions (as some insurers do) would amount, as pro-choice advocates note, to a restriction on the availability of abortion.

Here is the germ of a pro-life strategy to restrict the number of abortions, with the potential of saving untold numbers of lives:

Federal funds for abortions are now restricted to cases involving rape, incest or danger to the health of the mother. Abortion opponents say those restrictions should carry over to any health insurance sold through a new marketplace envisioned under the legislation, an exchange where people would choose private coverage or the public plan.

Abortion rights supporters say that would have the effect of denying coverage for abortion to millions of women who now have it through workplace insurance and are expected to join the exchange.

If a strong provision of the bill could be added that would forbid insurance companies that are part of this government system to fund abortions, would that make you willing to support it?