Can I collect unemployment if I quit my job because I have no one to watch my child? I have a 6 week old baby and there is no one to watch her and my boss told me that I either return on the next business day or I have to quit. Hi, Have you looked for childcare? .. By the way, do not quit. Your employer cannot require you to quit .. but they can fire you and that’s what they are talking about doing. Are you on FMLA?