The bill also specifies only physical health concerns as acceptable reasons for an abortion after the 20-week limit. That would put into place the narrowest health exception in the nation, as mental health isn't included. Interpretation of current law allows for mental health exceptions.
Borgmann, the law professor, can envision problems with this narrow health exception clause.
Imagine, she said, a woman who finds out after the 20-week mark that her baby lacks a brain, meaning the fetus isn't viable and will never become viable.
"In that circumstance, the woman would be unable to get an abortion," Borgmann said. "And a woman in that circumstance, one could imagine, would undergo severe emotional trauma having to carry that pregnancy all the way to term, having people as her about the pregnancy, whether she's named the baby."
In short, Borgmann said, the bill as proposed is unconstitutional and would surely face challenge in court -- a challenge she predicted the state would lose.
"So I think if the legislature wants to pass this bill they should do it with eyes wide open" knowing that they'd face costly legal fees down the road, she said.
The bill could put Nebraska on the national stage in the abortion debate for the second time in recent memory. A similarly controversial bill, banning late-term abortions, which are medically dubbed intact dilation and extraction (D&X) and known to anti-abortion activists as "partial-birth" abortions, went through the Nebraska legislature in 1997.
The U.S. Supreme Court, however, held the ban unconstitutional in 2000.
The setback for abortion opposition didn't last long: In 2003, the federal government outlawed D&X procedures, and the U.S. Supreme Court upheld the law's constitutionality in its 2007 ruling on Gonzales v. Carhart.
Dorothy Yeung, legislative counsel for National Right to Life, which supports the bill, said the new bill could mark a turning point for abortion legislation across the nation.
"We strongly believe that, upon the bill's passage, other states will follow it," Yeung said.
Janet Crepps with the Center for Reproductive Rights sees it another way: "It's essentially the legislature trying to practice medicine."
And, she added, "It should not be the job of the legislature to pass bills that they know are unconstitutional."
ABC News on Campus reporters Alina Selyukh, Andrew Mach, Morgan Demmel and Brandi Kruse contributed to this report.