Groups representing teachers and school boards told a Senate committee last week that it would be impossible to implement the measure without money to pay for it. Most schools will see state funding cuts or freezes next year.
"We can't solve every social problem at the school door," said Darold Johnson of the Ohio Federation of Teachers. "We need to do what we do well, and that's educate."
Jeff McCuen, treasurer of Worthington City Schools near Columbus, said the 30-minute exercise requirement would cost the district $4 million and take time away from core classes.
Other provisions in the bill would increase nutrition standards for a la carte food and beverages served in schools and require students to get body-mass-index screenings.
State Sen. Kevin Coughlin, a Republican from Cuyahoga Falls, agreed to take the exercise requirement out of his bill and instead allow districts to obtain a waiver. But he added that society rightfully asks a lot of public schools.
"While I share the view that parents have responsibilities on all these things, I can also have the view that our schools should be doing the right stuff while our students are in there nine months a year, seven hours a day," he said.
One in three American children is overweight or obese, increasing their risk of developing diabetes, heart disease and other illnesses, and contributing to high health care costs.
First lady Michelle Obama has made a campaign against childhood obesity. A government panel issued a report last week recommending 70 specific steps that all levels of government, the private sector, schools, parents and others can take.
Some of the recommendations call for updated federal nutrition standards for meals served at schools and more school-based nutrition education.
Obama has said her goal is to solve the problem within a generation so that babies born today can come of age at a healthy weight.