MIAMI — Democratic National Committee chair Debbie Wasserman Schultz has spent the last week sparring over reproductive rights with Kentucky Republican Sen. Rand Paul, who challenged her to say “if she’s OK with killing a seven-pound baby that is not born yet” when pushed to clarify his own position on rape, incest, and health exceptions for the abortion. And while the Florida congresswoman told msnbc she’s all too happy to go another round, she added that the issue would not ultimately determine who wins the presidency in 2016.

“Whether they happen to be pro-choice or what their position is on a host of important, but not central, issues isn’t going to drive their vote,” Wasserman Schultz said, saying the economy would be the main issue in the campaign.

WATCH: Rand Paul battles with reporters

“Voters are going to go to the polls and they’re going to choose who they want for president based on who has their back, who they believe has their back, and whether they perceive the candidate they’re choosing for president is going to help them reach the ladders of success,” she said.

Wasserman Schultz’s remarks were notable given the disastrous 2014 midterm election in which Democrats in several top races tried unsuccessfully to cast their GOP opponents as extremists on social issues. In the most prominent case, then-Colorado Sen. Mark Udall relentlessly attacked GOP opponent Cory Gardner for once supporting a “personhood” amendment that would ban certain forms of contraception. Gardner ended up winning the Senate seat anyway.

Wasserman Schultz’s spat with Paul began after the senator, who is strongly anti-abortion, got “testy” with an Associated Press reporter who pushed him to say whether he’d ban the procedure even in cases where a pregnant woman’s life was threatened or the pregnancy was the result of rape or incest. Paul declined to say.

Opposition to a rape exemption has been a stumbling block for previous Republican candidates, most notably failed senate candidates Todd Akin and Richard Mourdock in 2012. The DNC drew attention to Paul’s hedging on the issue and a New Hampshire reporter pressed him further, prompting Paul to refocus the argument against Wasserman Schultz.

“Here’s the deal—we always seen to have the debate way over here on what are the exact details of exemptions, or when it starts,” Paul said. “Why don’t we ask the DNC: Is it okay to kill a seven-pound baby in the uterus? You go back and you ask Debbie Wasserman Schultz if she’s OK with killing a seven-pound baby that is not born yet.”

Wasserman Schultz responded in a statement that she would “support letting women and their doctors make this decision without government getting involved – period” and again urged Paul to answer the original question.

The back-and-forth earned Paul cheers from social conservatives, who have urged their candidates to stop playing defense over exceptions on abortion bans and instead challenge Democrats on issues where public opinion leans more in social conservatives’ direction, like whether second trimester abortions should be legal. The Republican National Committee sent a statement to reporters decrying Wasserman Schultz’s “disregard for life” while an array of conservative commentators urged Paul to keep the argument going.

RELATED: DNC orders ‘top-to-bottom’ election review

“Sounds like her answer is yes, that she’s okay with killing a seven-pound baby,” Paul told CNN’s Wolf Blitzer.

For her part, Wasserman Schultz hit the ball back into Paul’s corner when asked whether voters might be uncomfortable with certain types of abortion procedures, as Paul and social conservative groups suggest.

“I answered his question specifically: We support a woman’s right to choose and we don’t support government interference between her and her doctor,” she said. “The way he tried to characterize that was to deflect and not answer the question he was asked. We still didn’t get an answer.”

She did not sound too concerned about how her exchange with Paul might play politically.

“If that’s what he thinks is the central issue and priority for the American voters and will drive the ultimate choice they make, then he’s more out of touch than I thought,” Wasserman Schultz said.