Can I get a caregiver for twelve dollars an hour?

It all depends on what is needed of the caregiver. Would the caregiver be a "companion sitter" or would the person needed to be highly skilled depending on the patient? The higher the skill, the higher the hourly rate. But then again, it depends on where you live and what is the going rate for different levels of caregiving.

Now if you hire outside of an Agency [an Agency would cost much more], don't forget you would need to add a "workman's comp" rider to your homeowner's insurance in case the caregiver gets hurt on the job. And you would need to prepare an employment agreement which says how many hours are needed, what are the duties, and what is the hourly rate paid.