Ohio Abortion Bill Poses Biggest Challenge to Roe v. Wade Yet

Arizona is considering laws that would ban abortions on the basis of the race or sex of the fetus, and prevent state money from going toward abortion, either directly or indirectly.

Experts say state governments have tried to circumvent the federal law for years.

"It's not really new. Ever since the 1980's, there have been repeated sallies by opponents of Roe v. Wade to see what holes they could puncture in the shield for women's reproductive freedoms," Tribe said. "This is simply another wave in an ongoing sea of challenges."

March For Life Rally Activists Demand Tougher Laws Watch Video

Santorum: Obama Abortion Stance 'Remarkable For A Black Man' Watch Video

Ariz. Hospital Stripped of Catholic Status Watch Video

What's different now, though, is that the wave in November that brought in droves of conservatives into state legislatures may increase the number of anti-abortion bills, and essentially pave the way for a Supreme Court challenge sooner than many had predicted.

On the national level, a bevy of new members of Congress are aiming to tighten federal abortion regulations further. At least three different bills dealing with abortion have been introduced in the Republican-dominated House.

Under current law, known as the Hyde Amendment, no funds appropriated to the Department of Health and Human Services can be used to pay for abortion services. But some lawmakers say the Hyde Amendment doesn't go far enough and that the new health care law opens the door for federal funding of abortions through state-based exchanges.