The slaying of Laci Peterson (search) has a legacy on Capitol Hill. This week the House will take up a bill in her name that would make it separate federal crimes to injure or kill both a woman and her fetus.

The Unborn Victims of Violence Act (search) is also being called Laci and Conner's Law, linking it to the highly publicized death in late 2002 of Laci Peterson and her fetus, whose body was found with plastic tape around its neck. Laci planned to name the boy Conner when he was born. Her husband, Scott Peterson (search), is on trial for their murders under California's unborn victims law.

Pro-life groups hope that in the wake of this tragedy, Congress will pass legislation protecting the rights of unborn fetuses, while abortion rights advocates fear this legislation will encroach on women's reproductive rights.

The bill's House sponsor, Rep. Melissa Hart (search), R-Pa., said she is trying to bring federal law in line with the 28 states that have laws covering the unborn.

The Peterson case "certainly does give it a bit of momentum and cast light on it that wasn't there before," said Lee Cohen, Hart's press secretary.

Although Cohen said the Peterson case did not play a role in Hart's introduction of the legislation, he said the congresswoman has noted that the tragedy "puts a face on it."

Laci's mother, Sharon Rocha, has been active in pushing the legislation, including writing letters to lawmakers believed to be on the fence.

The case puts "more pressure for members to vote in support of it. It's such a high profile case that it can't help but push the issue," said Jayd Henricks, director of congressional relations for the pro-life Family Research Council (search).

Already passed twice by the House, in 1999 and 2001, the measure is expected to win approval again when it comes up Wednesday or Thursday.

The Senate, with its stronger abortion rights forces, effectively ignored the proposal in the past. This time, Senate Majority Leader Bill Frist, R-Tenn., has promised to take it up soon.

The bill, he told a group of conservatives recently, "recognizes that when a criminal attacks a pregnant woman and kills her unborn child, he has claimed not just one, but two, precious human lives."

The legislation is regarded by conservative groups as vital.

"It's the most important issue to us this year," said Douglas Johnson, legislative director for the National Right to Life Committee (search).

Johnson cited polls showing that 80 percent of the public believes there should be a law recognizing the killing of a fetus as a homicide, but he said passage is not certain because "we still have adamant, vehement opposition by the abortion rights advocacy.

Opponents see the legislation as another attempt, after last year's ban on partial-birth abortion (search), to curtail abortion rights.

"We believe that it is a deceptive and callous attempt to undermine the right to choose," said Evelyn Becker, spokesman for NARAL Pro-Choice America (search).

The concern is that giving a zygote, an embryo or a fetus the same rights as a person could lead to future assaults on the Roe v. Wade (search) court decision affirming a woman's reproductive rights.

Certain forms of contraception could be banned or an airline might refuse to sell a ticket to pregnant women out of fear of being liable for a miscarriage, abortion rights groups said.

Rita Smith, executive director of the Denver-based National Coalition Against Domestic Violence (search), said her group tried to work with lawmakers writing the legislation to make it more about protecting women. "They wouldn't go down that road. This seems to be more about trying to undo abortion," she said.

Rep. Zoe Lofgren, D-Calif., and other opponents of Hart's bill favor a substitute that would increase penalties for attacks that lead to the interruption of a pregnancy but do not confer separate legal rights to the fetus. That version is not expected to prevail in the House.

Opponents said it would be the first federal law to recognize a fetus at any stage of development as an independent being. Hart argued that fetal rights, such as inheritance rights, have plenty of precedent in law.

The Bush administration, which supports the unborn victims bill, took its own initiative on fetal rights in 2002 when it ruled that "unborn children" were eligible for health care from the moment of conception under the State Children's Health Insurance Program (search).

Fox News' Peter Brownfeld and The Associated Press contributed to this report.