Unlikely. While I do not practice in Michigan, I cannot imagine that the laws in that state would allow eviction for a late utility bill. You may have a lease provision that addresses this issue, but even then it may not be enforceable. You should definitely consult with a local landlord-tenant lawyer asap -- and check out the following link for more basic information:
DISCLAIMER: I am not your attorney until you 1) sign a fee agreement with me, and 2) pay a retainer pursuant to said agreement. The response given does not create an ongoing duty to respond to questions. The response does not form an attorney-client relationship. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might change. Attorney is licensed to practice law only in Oregon (attorney has resigned from the Arizona bar, but may be reinstated upon application).
If your lease requires that you pay the water bill, then the water bill is an additional part of your rent. The lease probably says you will pay the water bill when due, in which case, if you did not pay the water bill when it was due, the landlord can give you a seven day notice of non-payment and file a suit to evict you the same as if you did not pay the rent. It is unlikely that your lease states that you will pay the water bill when you get a shut-off notice.