Can you be too poor to tithe?

My husband and I are having a baby in three weeks, so we're a family of three all living on one salary--my husband's. He doesn't make much money, so little that we actually get Medicaid and WIC from the state. We have the Internet at our house, because my husband has to have it for work, and we only have basic cable. We attend church regularly, but since we got married last year we have not given 10 percent. Living on such a small income, sometimes bills that need to get paid cannot be paid. We hope to bring in more money a few months after the baby is born, but we haven' been able to for a few months b/c I have been on bed rest. My husband suggested today that we start tithing 10 percent of our household income. I want to do what's right, but it makes me nervous to contemplate not being able to pay some of our bills so we can tithe 10 percent. I have trouble thinking that God would approve of such a situation. I know that tithing goes to the poor and needy--and frankly we are the poor... We occasionally get food from a community food bank, and we are barely able to afford food nutritious enough for a pregnant woman, even with WIC. Should we put ourselves in a situation where we are even more strapped financially in order to meet this 10 percent tithe requirement?