Republican senators facing primary challenges are rallying behind the most exhaustive congressional push to restrict abortion rights in a decade.
Eleven of the 14 GOP senators up for reelection next year support a new bill to ban the fraction of abortions that take place after 20 weeks of fetal development.
"In light of medicine and what we know about the unborn child in 2013, is it time to do more [to stop abortions]?" Graham asked. "We expect a robust debate."
The bill stems from an assertion that fetuses feel pain after 20 weeks, and follows the murder conviction of Philadelphia abortion doctor Kermit Gosnell, whose trial drew attention to the practice of late-term abortions.
The "fetal pain" premise, which has inspired tighter abortion laws in at least 10 states, is disputed among medical experts and widely challenged by supporters of abortion rights.
Graham's bill had 35 co-sponsors as of Thursday afternoon, including some of the Tea Party's top Senate targets for 2014: Thad Cochran (R-Miss.), Pat Roberts (R-Kan.) and Minority Leader Mitch McConnell (R-Ky.). Sen. Mike Enzi (R-Wyo.), who is facing a strong Republican opponent in Liz Cheney, is also supporting the bill.
Republican lawmakers are seeking to bolster their conservative credentials in the early stages of the midterm cycle, which could see veteran members ousted.
For those in red states, like Enzi, a primary challenge is often more risky than facing a Democrat in the general election.
Sen. Lamar Alexander (R-Tenn.), who is facing conservative state Rep. Joe Carr, was immediately singled out Thursday for failing to sign on to Graham's bill.
“I’m strongly pro-life and believe it’s imperative the Senate pass this important piece of legislation," Carr said in a statement.
"This legislation is too important to the pro-life movement for [Alexander] to stay on the sidelines."
GOP candidates are also guaranteed to face attacks on abortion and birth control policy from the left next year.
Women's health issues became the downfall for would-be GOP senators Todd Akin (Mo.) and Richard Mourdock (Ind.) in 2012, and were seen as solidifying the gender gap that doomed Republican Ken Cuccinelli in the race for Virginia governor this week.
Echoing their messaging from the last election, Democrats quickly jumped on Graham's bill Thursday as an attack on women's health and rights.
"We're not going to take away a woman's ability to make her own decisions about her own healthcare and her own body," Sen. Patty Murray (D-Wash.) said on the Senate floor.
"Women are not going back to the time when laws forced them into back alleys and made them subject to primitive and unsanitary care."
This charge was widely echoed by groups like Planned Parenthood, which called Graham's bill "dangerous and extreme."
Carol Tobias, president of the National Right to Life Committee, sought to fend off the criticism.
"Do they not know how big and how developed a baby at just 20 weeks is?" Tobias said. "[We] certainly are not anti-woman. We are real women, protecting very well-developed, unborn children — half of whom are women."
Graham's bill has support from two of the Senate's four Republican women — Deb Fischer (Neb.) and Kelly Ayotte (N.H.) — but neither was on hand for a press conference Thursday.
Instead, Graham and co-sponsoring Sen. Rob Portman (R-Ohio) stood beside six women leaders from the anti-abortion movement.
The House version of the bill passed on a mostly party-line vote of 228-196 in June. Six Democrats supported the measure, while six Republicans opposed it.
Graham acknowledged his legislation does not yet have 50 votes in the Senate but deflected when asked if his leadership on the bill had to do with the politics of his next election.
"I came into the political arena pro-life, and I will leave pro-life," he told reporters. "Whether I will leave next June or at some later period will be up to the voters."
The 20-week ban includes a handful of narrowly tailored exceptions, all of which are required to result in a live delivery whenever possible.
Under the bill, a woman could only obtain an abortion after 20 weeks if she became pregnant from a rape; if she was a victim of incest and a minor; or if the procedure was necessary to save her life.
In a case of rape or incest, the crime would have to be reported to the appropriate authorities in order for the abortion to proceed.
And in all exceptions, a physician would have to perform the abortion "only in the manner which … provides the best opportunity for the unborn child to survive" unless doing so threatens the woman's life or physical health.
The requirement "applies to any of the exceptions," said Graham spokeswoman Alice James.
The bill does not allow for abortions in cases of severe fetal anomaly.
Abortion-rights groups argue this exception is vital given that ultrasound scans after 20 weeks can reveal fatal problems with the developing fetus. Opponents call those cases rare.
— Ramsey Cox and Cameron Joseph contributed.