The only real advice I (or anyone here) can give you is personal advice--this is not legal "advice", it's just information. For actual advice, you need to retain an attorney. Realistically, if you're not married, he does not have any legal or financial obligations toward you. If he's the father of your daughter, he'll have to pay child support for her, but that's the extent of it. If this is related to a family violence situation, you might be able to find some help through a local agency that specializes in helping abused women get back on their feet, but otherwise you're going to have to rely on family and friends until you can manage to get a job. On the bright side, evictions are very hard to manage procedurally, and of he's trying to do it himself, he'll probably screw it up. For example, it's not like he can have the police come throw you out once those three days are up. That's just the notice he has to give you before he can go down to the JP court and file an eviction proceeding with them, and he may not know that. But you're not likely to able to stall for long, and if the situation is unpleasant, exposing your daughter to that is not a good thing. If he's being at all reasonable, perhaps a better approach would be to tell him you'd like to sit down and talk about it, then explain that you do know that he is not legally obligated to help you and that you know you need to get a job now and support yourself, but that while you will immediately start trying your hardest to accomplish that, you can't do it immediately. See if perhaps you can negotiate with him for a little time to get your act together. Sometimes arrangements can be made where parties in this situation who can't afford to separate will agree to just stay out of each other's way until things can be resolved. Even if that involved you sleeping in your daughter's room and only using the kitchen at certain hours or something, it would be being homeless, wouldn't it? And in exchange perhaps there's something you could offer to do for him that would placate him and make him willing to let you stay for a bit, whether it's things around the house, help with errands, or whatever would make a difference to him. Good luck.
If you two have held each other out as man and wife, and if you satisfy other Texas requirements, you may qualify for a common law marriage. Seek legal counsel immediately regardless. Depending on your facts, an attorney may be able to develop a legal theory to claim benefits. Even if there is no common law marriage, you may be able to argue that you had a contract for you to maintain the home front and you complied.