If my mother pays me for taking care of her, will those assets she pays me be effectively spent down for Medicaid?

Medicaid doesn't expect applicants to have no expenses. As long as they are spending their money on themselves that is perfectly legitimate. If she is paying you way above going rates in your area, that might be considered gifting, but if the amounts are in line with what she would have to pay someone else, all should be well. Having the contract checked over by an Elder Law attorney would be a smart precaution.

Check out the Medicaid laws in your state because they may deny based on what's you've posted. And do hire an attorney.

I've seen responses on this site that indicate you can do this. Please work with an elder care attorney so that the contract is drawn up correctly to protect both you and your mother. Good luck!