The chairs of the state’s two leading political parties met for the first time this week, when the pair of newly elected politicians found plenty to disagree about.

Amy Carnevale, elected in January to replace Jim Lyons as the head of the MassGOP, and Steve Kerrigan, who last week won an unopposed contest to lead the state’s Democratic party, both joined WGBH’s Margery Eagan and Jim Braude on Monday to discuss plans to grow their parties in a state dominated by unenrolled voters.

Carnevale said her first order of business is to rebuild the MassGOP, which controls few seats in the Legislature, no constitutional offices or congressional seats, and last year lost the governor’s office.

“My primary objective first is to stabilize the party and work on the messaging of the party. It is clear that the party has gotten off track in recent years,” she said.

Kerrigan, who oversees a state party in full control over all parts of the government, said it’s his job to explain the value of the party to voters in a state with more independent residents than both political entities combined can count as enrolled.

“My old boss Ted Kennedy used to always remind us to never rest on our laurels and so there’s still lots of work to be done. In my voting lifetime we’ve had two Democrats elected governor of Massachusetts and I’m 51,” Kerrigan said.

The conversation between the pair began amicably but became a debate — if not an argument — over access to abortion, and after Carnevale said hers is the party of freedom and that the economy is doing worse under President Joe Biden than it was under former President Donald Trump. Kerrigan laughed at the last assertion.

“I’m laughing just because of the 12 million new jobs that have been created under Joe Biden; the lowest unemployment rate in generations. I’m laughing because that talking point just doesn’t pass the laugh test,” he said.

Carnevale said that a lot of people in Massachusetts aren’t feeling very encouraged by that data.

“I think if you talk to a lot of Bay State voters today they are suffering under inflation, the cost of eggs, the cost of gas,” she said.

Carnevale told the Herald she joined Monday’s NPR program, which typically broadcasts to a more liberal audience, not to argue with her counterpart but to spread the conservative message.

“If the Republican Party is going to get back to winning elections in Massachusetts, party leaders and candidates cannot be shy about taking our message to both unenrolled voters and Democrats,” she explained.