My daughter wishes to care for her grandmother. Can she get paid for her services in the state of Michigan?

Are you asking if there is a government program? Medicare does not pay for in-home help from family caregivers. Medicaid waiver programs in Michigan might pay for some help if the grandmother is on Medicaid and qualifies for assistance. Any money paid to the granddaughter would be income and taxes etc. would be owed on it. You can check to see if grandmother qualifies for Medicaid by checking with your state agency. It won't be 40 hours per week in most cases (usually 3-4 hours per day max), and the job may not have benefits depending on the agency. If you don't go through an Agency to provide care, someone will have to report income and submit proper taxes to IRS and MI. You can start by checking with Michigan Medicaid offices - here is a link
http://www.michigan.gov/mdhhs/0,5885,7-339-71547_4860---,00.html