For the past three years, anti-abortion activists have worked methodically to across the country to test the limits of Roe v. Wade by advancing a variety of new laws limiting access to abortion services. On Tuesday, a federal court in Wisconsin begins consideration of whether one of those laws goes a step too far.

U.S. District Judge William Conley this week will hear at least four days of arguments for and against a state law in Wisconsin that requires abortion providers to have admitting privileges at a hospital within 30 miles of their clinic. A version of this law, passed in Wisconsin in June 2013, has been adopted in seven other states. As recently as last week, the Louisiana legislature sent a version of the bill to Gov. Bobby Jindal, who has promised to sign it into law. Other states like Oklahoma are also considering it.

Yet in multiple cases, courts have put the laws on hold so that the legal basis for the new restrictions can be carefully considered. While the 1973 Roe decision gave women the right to obtain an abortion, the 1992 Supreme Court Case Planned Parenthood v. Casey offered a more nuanced ruling: the Supreme Court said that the government can impose restrictions on abortion services so long as they don't impose an "undue burden" on women.

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Conley has expressed skepticism that the Wisconsin law can meet the standards set by Casey. When he put the law on hold in August, the judge wrote "that defendants are not likely to succeed in demonstrating that the admitting privileges requirement is reasonably related to maternal health; and plaintiffs are likely to succeed in demonstrating that the admitting privileges requirement will unduly burden women's access to abortion services in Wisconsin, at least in the near term."

Wisconsin's two abortion providers, Planned Parenthood of Wisconsin and Affiliated Medical Services, say the rule would cause two of four abortion clinics in the state to close and cut the capacity of a third clinic by 50 percent.

Admitting privileges at a nearby hospital can be hard to obtain for a variety of reasons: For instance, some hospitals will only grant admitting privileges to doctors who meet residency requirements or can guarantee referring a minimum number of patients. Yet doctors who provide abortions often travel from town to town to provide the service. Earlier this month, abortion clinic operators challenging the law in Alabama said that their staff and physicians are often harassed -- that makes it difficult to find local doctors willing to work there.

Conley, wrote that the rule in Wisconsin "will have the effect (if not also the purpose) of presenting a 'substantial obstacle' to the provision of those services, at least in the near term."

In fact, the supporters of the law have no qualms about admitting that it is their goal to create obstacles for women seeking out abortion services. The anti-abortion rights group Americans United for Life has helped states across the country draft their own versions of the bill to do just that.

"I recognize that goal," Louisiana state Rep. Katrina Jackson, a Democrat who sponsored such legislation in her state, told CBS News' Anna Werner. "But I also understand that [Americans United for Life] and many others are doing so in the confines of Roe v. Wade. And to the extent that they're doing it in a constitutional manner, then I stand with them."

In March, the 5th Circuit Court of Appeals agreed that Texas' version of the law "on its face does not impose an undue burden on the life and health of a woman." The appeals court, in effect, accepted the premise that traveling far distances to reach the remaining abortion clinics in a state is not an "undue burden." The Wisconsin government is making the same case.

"According to Plaintiffs, because capacity is reduced, women will be forced to drive farther and wait longer. None of these circumstances, even if true, would create an undue burden that prevents a significant number of women from obtaining an abortion," Wisconsin Attorney General J.B. Van Hollen has argued.

The ongoing court challenges suggest the issue will eventually make its way to the Supreme Court. In November, the Supreme Court's four liberal justices said they were interested in considering the constitutionality of the law, regardless of which way the appeals court ruling in the Texas case went.

In November, the four dissented from a high court ruling that upheld the 5th Circuit's decision to allow Texas to enforce the law while the appeal proceeded.

"It is a question, I believe, that at least four members of this court will wish to consider irrespective of the Fifth Circuit's ultimate decision," Justice Stephen Breyer wrote in a brief opinion that was joined by Justices Ruth Bader Ginsburg, Elena Kagan and Sonia Sotomayor.