"Was he a relevant player at Lehman?" asked Strickland. "And, if he wasn't, what did he do to deserve a bonus of over $400,000 at a time when the company was getting ready to go down the tube? I just think those are fair questions for me as his opponent to ask."
Beyond attacking Kasich for his work at Lehman Brothers, Strickland is also chiding him for flirting with the gradual elimination of the state income tax.
Kasich has said he sees the idea, which he has not fleshed out in detail, as a game-changing economic strategy that could attract investment and new jobs to Ohio, which has been economically ravaged by the loss of manufacturing jobs.
Strickland said the financial practices at Lehman Brothers, where they were selling their own loans to themselves to make it look like they had more money and less debt, and Kasich's tax plan are both part of a "hot dog approach to the economy."
"The state income tax over the last 10 years has been 46 percent of total revenue. To talk about eliminating the state income tax -- say he did it in eight years -- it would represent a devastating, cataclysmic result on libraries, schools, public safety, everything the state of Ohio has a responsibility to support," Strickland said. "All the public services would be decimated."
Strickland, one of Hillary Clinton's most prominent backers in 2008, said he sees the fight for the Ohio governor's office as having the potential to reverberate beyond the Buckeye State.
Kasich, a former chairman of the House Budget Committee, briefly explored running for president in 2000, and Strickland said his GOP rival may still have his eye on the White House.
"I think that's a reasonable assumption," said Strickland when asked about the prospect of Kasich running for president again, possibly in 2016. "I don't know what's in his heart, what's in his mind. But he's a very ambitious guy, so I think it's reasonable to assume he may still harbor those desires to be president."
ABC News' Matt Loffman contributed to this report.