By Sarah Parnass, ABC News

“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 [Plutarch] 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.

Newark NJ mayor Cory Booker is an activist and hero who ran into a burning home to save residents. He regularly communicates with constituents through social media – and is a partner in Waywire, a start-up.

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.

[On November 21st] 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.

[Rucha Gadre, director of a food bank,] took the food stamp challenge earlier this year and 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.

The average food stamp user receives $5 a day ($35 a week) to buy groceries. Here’s what Representative Bob Brady of Philadelphia bought during his participation in the city-wide challenge.

“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.”

Read a critique of Booker’s food stamp experiment here.

Want to take the challenge yourself? Find out who is taking/has taken the Food Stamp Challenge in your area. Get tools for simple ways to  initiate a community campaign, like the Paper Plate Campaign. Let ABHM know how it goes for you by writing a comment below.