Graham was discussing the topic on the first day of Supreme Court nominee Brett Kavanaugh's confirmation hearing. Some Democrats have seized on Roe v. Wade, the landmark ruling legalizing a woman's right to abortion, in opposing Kavanaugh's nomination.

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Trump nominated Kavanaugh in July to replace retiring Justice Anthony Kennedy, who was the fifth vote on a 1992 case that upheld the ruling.

Democrats have warned about Kavanaugh possibly joining other justices on the court in a ruling on Roe v. Wade after Trump said during the presidential election that his nominees would overturn the 1973 decision. Graham noted that Clinton during the presidential campaign said she had several "litmus tests" for Supreme Court nominees, including on abortion.

"We’ve got to make sure to preserve Roe v. Wade, not let it be nibbled away or repealed," Clinton said at the time.

Graham on Tuesday jokingly dared Democrats on the Senate Judiciary Committee, several of whom are considered potential 2020 White House contenders, to disagree with Clinton.

"Anybody running for president over there, I dare you to disagree with her. You'll wind up like I did, getting 1 percent," Graham said, referring to his failed presidential bid.