Actually, there could easily be a duty to repair the water flow to a kitchen sink. Landlords do have a duty to maintain plumbing.
"Not making ice properly" suggests that the fridge is making ice; but even if we assume that it stopped working after you moved in, and that the landlord has a duty to repair appliances provided as part of the rental arrangement, the failure to repair an ice maker in an otherwise working refrigerator is not going to constitute a material violation of the lease.
As was previously indicated, if you're a month-to-month tenant your tenancy can be terminated upon proper notice (generally 30 days or, if you've been a tenant for more than a year, 60 days); if you're in a rent control community you can check to see if you have any additional protections under the governing ordinance.

