The argument for the 20-week rule is that developing fetuses can feel pain after that point, The New York Times reported Friday.
Doctors dispute whether that is true, but polls show 61 percent of the public support legal abortion in the first trimester, a share that drops sharply later in pregnancy.
"Our mission is to restore legal protection to unborn life from the moment of conception," Julie Schmit-Albin, executive director of Nebraska Right to Life, told the newspaper. "This is a marathon."
At least 10 states have passed laws setting the limit at 20 weeks. Judges have blocked such laws in three states where they have been challenged.
A national bill passed the House in June but is widely considered to have no chance of Senate passage, and the White House has said President Barack Obama would veto the bill.
The Supreme Court's 1973 Roe vs. Wade decision found abortion is a private matter up to the point of viability -- about 24 weeks into a pregnancy. Abortion opponents hope the court, now split between conservatives and liberals, with conservative Justice Anthony Kennedy as a swing vote, will rule in favor of 20 weeks.
In practice, the 20-week rule only shaves two weeks off the time because of different ways of calculating when a pregnancy begins, but abortion rights activists say reproductive choice is on a slippery slope.
"These laws are cloaked in the language of two-week increments, rather than banning abortion at conception or other more radical measures," Suzanne B. Goldberg, director of the Center for Gender and Sexuality Law at Columbia University, told the Times. "They are cutting back on women's constitutional rights, but less dramatically, so they trigger less alarm across society."