NEW YORK — Millions of American women will face tough choices about abortion coverage if restrictions in the House health care bill become law, both sides in the abortion debate agree.

Divisions over abortion are a major obstacle in President Barack Obama's push for health care overhaul, with both sides arguing over how to apply current law that bars taxpayer dollars for abortions in a totally new landscape. Under pressure from the Catholic Church and abortion foes, the House added tough restrictions to its version of a health care bill.

The measure would prohibit the proposed new government-run insurance plan from covering abortions except in cases of rape, incest or to save a mother's life, and bars any health plan receiving federal subsidies in a new insurance marketplace from offering abortion coverage. If women wanted to purchase abortion coverage through such plans, they'd have to buy it separately, as a so-called rider on their policy.

"It forces insurance companies and women to navigate a series of chutes and ladders to get abortion coverage at the end of the day," said Donna Crane, policy director for NARAL Pro-Choice America.

The amendment's proponents says its goal is simply to ensure that a long-standing ban on using federal dollars for elective abortions is extended to coverage plans arising from new health care legislation.

Rep. Bart Stupak, D-Mich., an abortion foe, insisted the amendment is not a dramatic change in current law, offered to negotiate if his critics could convince him otherwise, and said it leaves ample alternatives for women to obtain coverage if they use their own money and are willing to buy a separate, add-on plan.

"If you really still want this coverage, you can have it," he said. "The only difference is that more people will have to make that decision that they didn't confront before. ... More people are going to have to choose, 'Is this a benefit I want?'"

Crane and other abortion-rights advocates say the amendment would make it harder — in some cases perhaps impossible — for millions of women to have health insurance that covers abortion. They depict it as one of the gravest assaults ever on American women's reproductive rights.

Two large groups of women would not be affected by the amendment: low-income women already ineligible for abortion coverage because they rely on federal Medicaid funds for health care, and women who have abortion coverage through the private plans of their own or their husbands' large employers. Most Americans currently have employer-sponsored coverage.