No, you can become a naturalized citizen even if you are receiving food stamps or other forms of public assistance. Also, you may be eligible for a fee waiver when you apply.
Some people run into problems if they lied about their income to get the food stamps and that is discovered by the examiner in the naturalization interview. If you are truly eligible for food stamps, there is nothing about which you need to be concerned.
Because you receive public assistance, you should be eligible for a waiver of the $680 naturalization filing fee. I have placed a link below where you can get more information.