It started with a quote from Plutarch.

"An imbalance between rich and poor is the oldest and most fatal ailment of all republics," Newark, N.J., Mayor Cory Booker tweeted Sunday night, not knowing that his reference to the Greek historian would prompt an online spat over governing philosophies and lead him to challenge a stranger to match him in living on food stamps for a week.

Booker, known for his charisma and tendency to respond to residents over Twitter, faced criticism for the quote. One tweeter accused him of wanting to redistribute wealth.

"We pay 4 HUGE back end govt programs: prisons, police, etc. If we invested in Schools, nutrition, etc we'd save $ & create wealth," Booker tweeted back.

Read about chef Mario Batali's food stamp challenge and his entire week's grocery list.

More than 415,000 families received assistance from NJ SNAP, New Jersey's food stamp program, in September. Almost 15 percent of those families live in Essex County, where Newark is located. Essex had one of the highest increases in the state in demand for SNAP benefits that month, with the number of families participating rising 9.1 percent in the year ending in September.

@MWadeNC , a user who identifies herself as a "Daughter of the American Revolution (DAR), fighting against any and all forms of socialism/communism.. Army Veteran, Army Daughter, Army Wife," responded to Booker, "nutrition is not a responsibility of the government."

Booker said it was a shared responsibility, to which @MWadeNC asserted that food stamps should be enough to enable a family to afford breakfast.

"Lets you and I try to live on food stamps in New Jersey (high cost of living) and feed a family for a week or month. U game?" Booker tweeted at @MWadeNC.

"sure, Mayor, I'm game," she replied.

Read the full exchange here .

The mayor's office has not confirmed that he will make good on the challenge, but in another tweet, he asked the University of Bridgeport to send him the rules for their SNAP Food Challenge and to referee his competition. Later, Booker tweeted that he'll consider going longer than a week and will start after Thanksgiving.

UB's event runs December 2-8 and requires participants to spend no more than $35 on all food and drinks without accepting free food from family, friends or coworkers. UB also asks those taking the challenge to post photos of what they consume that week on social media platforms and to make a video with their observations at the end of the week.

Rucha Gadre, director of Food Bank Services at Mercer Street Friends, said a family of four making under $3,447 per month in her county gets about $150 to $250 a month through NJ SNAP.

Gadre took the food stamp challenge earlier this year, and she said it was "very difficult."

"I think [Booker] will understand that the minimum benefit of $16 or trying to live on $30 for the whole week is not sufficient," Gadre said. "There's no way you could eat nutritious food."

Even if Booker sticks to the dollar limit, Gadre said the experience still might not replicate the exact experience of surviving on food stamps, because low-income families might not have the luxury of searching for the cheapest grocery stores.

"If you have a car and you have the ability of driving around…then that makes it easier," Gadre said. Not all of the families she encounters have their own cars and spending $2 or $3 on a bus doesn't always make sense, Gadre said.

Other mayors who have tried limiting their grocery money to food stamp levels include Las Vegas Mayor Carolyn Goodman, Philadelphia Mayor Michael Nutter and Phoenix Mayor Greg Stanton.

In his food diary for the week, Mayor Stanton ran into trouble on day four when he forgot to pack his lunch from home.

"I'm facing a long, hungry day and an even longer night getting dinner on the table, which requires making EVERYTHING from scratch on this budget," Stanton wrote. "It's only for a week, so I've got a decent attitude. If I were doing this with no end in sight, I probably wouldn't be so pleasant."

UPDATE 11/21/12: Today Mayor Booker tweeted that he would participate in the SNAP challenge from Dec. 4-11 and report back about the experience on LinkedIn, Twitter, Facebook and Waywire.