Took in a stray cat, and now am told to have it gone by the end of the day?

We took in a stray cat and have provided a loving home to her for the past week. My husband and I had an argument today, and I suppose to retaliate he has told me to get rid of the cat by the time he gets home tonight from work. He seemed like he loved the cat and was happy letting her sleep next to him every night, talked about how nice she was, etc. When I was at the vet a few days ago, a woman was talking about how the shelter was full, and there were unable to take in kittens she found. I am not sure what to do about this situation. We had even talked yesterday about having the cat spayed within a couple weeks to prevent any future pregnancy. Any advice? Thanks.