Cory Booker responded to critics of hisfood stamp challenge on"Piers Morgan Tonight" Friday, saying he hoped his actions would inspire a more heated debate.

The Newark, N.J. mayor is more than halfway through a week living on the monetary equivalent of food stamps. He had $30 for the whole week -- a mere $4.32 a day -- to pay for all of his meals and beverages.

While he's been lauded on Twitter for his efforts to highlight the struggles of some42 million Americans on food stamps, some have suggested he is misleading about how the program is designed to be used.

On Wednesday,CNN's Christine Romans took issue with Booker's challenge.

"It's not meant to be your only calorie intake source," Romans said. "'Supplemental' is the key. The government designs it so this is on top of what little money you might have, food pantries, soup kitchens."

Asked to respond to her comments, Booker said it was just "reality" that many Americans rely on food stamps to survive.

"There are many families -- and I talked to a group of security guard workers yesterday who make seven dollars and change, don't have health care benefits, so if they get sick, they have to either take days off of work and lose that money, or work through the sickness, who don't have retirement benefits, who find it hard at the end of the month to pay their rent, to buy their food, and are struggling," Booker said.

"She may think its a supplemental program, but for many Americans who are working even, this is the difference between going deep into food insecurity, not being able to provide for their families, and having a bridge to stability," Booker continued.

Booker is now on day five of his food stamp challenge. He has beentweeting,blogging andInstagramming his progress.

On Friday, he blogged that he had a terrible headache from lack of coffee and was rationing his food carefully so he wouldn't run out:

Today is the 4 day of my #SNAPChallenge and so far it has been the most difficult. I’m realizing more and more that my current daily food intake cannot continue at the same pace, and so my new focus is on smaller portions spread throughout the day.

This morning I had one apple for breakfast followed by a can of chick peas with seasoning and olive oil for lunch. My last meal of the day consisted of broccoli, cauliflower, black beans, corn casserole and a sweet potato which I ate in small portions between 2pm and 7pm this afternoon. I will likely not eat again until tomorrow morning in order to maintain enough food.

You can see Booker's groceries for the challengehere.