As many critics of the bill have pointed out, it is based on the false premise that fetuses can feel pain at 20 weeks--a political argument that has been debunked by science and medical experts.
At a press conference following the session on Thursday, Graham told reporters that he would "insist" that the bill gets a vote in the Senate, even if it did not have a chance of being signed into law by President Barack Obama.
"I am dying for that debate. I'm going to quite frankly insist that we have that debate," Graham said.
As the Center for Reproductive Rights noted on Thursday, abortion bans at 20 weeks "take critical medical decisions out of the hands of women and their trusted health care providers at a time when those services may be the best medical option for a variety of reasons."
That includes cases in which medical tests reveal fetal anomalies or other complications that could not be detected earlier.
"At a moment when women's access to essential reproductive health care is in greater peril than at any time since Roe v. Wade, Congress should be acting to alleviate the crisis, not worsen it," said Nancy Northup, president and CEO of the Center for Reproductive Rights, in a statement on Thursday. "While anti-choice politicians in Congress work relentlessly to criminalize abortion later in pregnancy, their counterparts in state legislatures are making it increasingly difficult or impossible to get safe, legal care even in the first trimester."
"This has to stop," Northup added. "It's time to advance legislation... that promotes access to the care and services supports women's health, safety, and empowerment, not bills like this one that insult women's dignity and threaten their lives."
Graham's bill has 42 Republican co-sponsors, including Senate Majority Leader Mitch McConnell.
However, if the bill does become law, recent legal rulings indicate that it may be challenged in the courts.
A federal appeals court in Idaho last month struck down a similar 20-week abortion ban, which the judges said violated a Supreme Court precedent protecting abortions up to the point of viability--around 24 weeks. Recent medical studies have shown that fetuses do not feel pain before 24 weeks, and possibly even later.
The bill could prove to be politically risky for the senator. As Politicopoints out, "Graham's effort threatens to hand political ammunition to Democrats trying to knock off GOP senators in purple and blue states that will decide Senate control after the 2016 election."
NARAL Pro-Choice America President Ilyse Hogue said Graham, who recently launched his 2016 presidential campaign, "is choosing to use his position in the Senate to advance an abortion ban to bolster his long-shot White House bid in a shameless play to early-state ultra-conservative voters."
"We have seen this playbook over and over from anti-choice Republicans up and down the ballot," Hogue added.
