"What we've got to do today is vote our conviction," said Republican Sen. Larry Martin on Tuesday.
The proposal allows prosecutors to seek the death penalty for sex offenders who are convicted twice of raping a child younger than 11.
Currently in South Carolina, murder is the only crime eligible for the death penalty.
The proposal was approved as part of a larger bill that sets minimum sentences and lifetime electronic monitoring for some sex offenders. The bill requires a third reading before moving to the House.
The U.S. Supreme Court ruled in a 1977 Georgia case involving an adult victim that sentencing someone to death for rape was unconstitutional.
A Louisiana law lets prosecutors seek the death penalty for rapists of children younger than 12, and the Louisiana Supreme Court found it constitutional because the U.S. Supreme Court ruling did not address the rape of a child.
The U.S. Supreme Court declined to review the statute.
Attorney General Henry McMaster said he believes South Carolina's proposed law would be found constitutional and that he would be proud to argue that case.
Sen. Vince Sheheen asked McMaster at a hearing before the vote if he worried such a law would persuade child molesters to kill their victims rather than leave witnesses.
"They do that anyway," McMaster said. "The state needs to take as strong a stance as possible."
Sen. Jake Knotts, chief sponsor of the bill and a retired law enforcement officer, said a death penalty sentence from South Carolina will likely become the test case before the U.S. Supreme Court.
"We have a chance to be a leader," Knotts said. "Let's do something about these predators ... Let our children grow up like you grew up."
University of South Carolina law professor Kenneth Gaines told the subcommittee Tuesday he believes the U.S. Supreme Court would find South Carolina's proposed law unconstitutional, relying mostly on whether a majority of states have similar laws, the Columbia State reports.
But McMaster said he believes many states will have followed South Carolina's lead by the time the Supreme Court gets a case to review.
Elsewhere, the Idaho Senate voted unanimously Tuesday for a bill that would prevent any convicted sex offender from going within 500 feet of a school where there are children under the age of 18 — with the exception of sex offenders who are parents, mail carriers or deliverymen.
Michigan's state senate voted overwhelmingly Tuesday to require that repeat child molesters and rapists spend life in prison with no possibility of parole, an effort to keep dangerous predators off the streets. The bill now heads to the House, which passed similar legislation two weeks ago.
And House and Senate negotiators in Kansas were at odds over whether sentencing discretion for sex offenders should rest with prosecutors or judges.