Can the Polizei do anything about unpaid rent before 60 days?

My landlord is really bad so I'm moving. I asked if I was going to get my security deposit back and I was told that 5000 euros is a small amount and I will probably have to pay more for damages. But I have not damaged the apartment.

I've had people tell me just don't pay the rent which I decided to do. The landlord is obviously pissed and threatened to call the Polizei but when I looked online, they can't evict until the end of the second month. What can the Polizei do before then?

I'm American living in Germany so English only, please!