The electronics chain employs 1,100 workers at its downtown campus.
Critics have blasted the idea, which comes at a time the city faces $77 million in red ink and has furloughed employees and closed swimming pools.
He also questioned whether it is a wise use of taxpayer money.
"In the past, we gave out incentives if a company actually creates something,” Schnurman said. “All Fort Worth is doing now is trying to maintain the status quo. And even the status quo is not a very good deal."
Backers of the incentives say Fort Worth already owes Radio Shack $13 million under its original incentive deal in 2002. The money would repay the company for public streets and other public projects when it built its headquarters.
"It's pay me now or pay me later,” said former Fort Worth Chamber of Commerce chairman Wes Turner. “We have to refund them and repay them the money they spent on infrastructure. A deal was a deal."
But Shnurman said the company is trying to change its 2002 deal, in which Radio Shack would get the incentives over a maximum of 30 years if it met certain requirements.
Instead, the company has slashed thousands of jobs and sold its downtown campus to Tarrant Community College three years after building it.
Meanwhile, news reports that Radio Shack is shopping for a buyer raise questions about whether or not the company will remain in Fort Worth at all, critics say.
Supporters of the incentives say if Fort Worth agrees to the new tax breaks, Radio Shack would be obligated to pay its lease for five years.