Will this cat ever be able to deal with my dogs? Please help!?

Do you have big dogs or small dogs. Are the dogs aggressive to the cat. The cat will get used to the presence of the dogs but may be leery. Always make sure that the cat can jump from one high area to another for her own feeling of safety. Thank you for taking her in. She doesn't need to be in the basement. This is just too confining when she is to be a member of the household. Let her roam around the house with the dogs in another room and slowing introduce each dog. Keep them on a leash during introduction so that the cat feels safe.