The hourlong debate, hosted by WSB-TV in Atlanta, comes two weeks from the June 20 runoff race, which has national implications and became the most expensive congressional election in history - with donors in both parties funneling tens of millions of dollars into the contest.
Georgia's minimum wage is $7.25 per hour, the same as the federal minimum wage.
But Handel downplayed her role.
Handel says Ossoff was "hand-picked by Nancy Pelosi", who would nearly certainly become speaker again if Democrats flip 24 Republican-held seats by next November. But she has not incorporated the President into her campaign messaging with the kind of zeal that Greg Gianforte, the Montana Republican who adopted Trump's "drain the swamp" campaign message and aggressive attitude toward reporters for his successful bid for an at-large House seat last month, did. At those events, Ossoff steers clear of Trump and blatantly partisan rhetoric that animates liberals like Hanson and Gray. Democrats were hoping to flip the 6th District blue with Jon Ossoff as he was on the same ballot as 17 other candidates, including eleven Republicans. What she needed to say was that not every job is meant to have a "living wage" because not every job is fitted for one person to raise an entire family on.
Ossoff says the growing and diversifying district is "ready for some fresh leadership. rather than divisive, nationalized politics". One commercial showing actors dressed in hippie garb, and cable cars in the streets of San Francisco, said California was "the leading funder of the Jon Ossoff campaign".
As Ferguson noted, Ossoff hasn't managed to avoid Trump completely during his campaign.
NAYLOR: Handel did not respond to repeated requests for an interview. Handel asked Ossoff, bringing to light that he lives outside of the 6th District.
"I prefer to think about what I'm running for", Ossoff replied.
"Handel supports what is not even a bill yet - something that has not been assessed by independent economists to understand its impact on growth and deficit", Ossoff said. "We need to be finding common ground, finding areas to work together".
The special election for Health and Human Services Secretary Tom Price's congressional seat in Georgia has gotten personal - and, at times, uncomfortable.
Both candidates have rejected the idea that the race is a referendum on President Donald Trump, but national issues dominated the debate. Ossoff says he wants to focus on the local community, and also accused Handel of hiding from the media.
Georgia Republican Karen Handel has a bad record on women's health.
He also attacked Handel for being "born and raised in Washington, D.C".
Handel has raised money with Trump.
The pair are only confirmed to make one more televised debate appearance together, Thursday evening on the Atlanta-based PBS station, WABE-TV/PBA 30.
"I do not support a livable wage", she said, painting her view as the "fundamental difference between a liberal and a conservative".