It is my understanding that in NY a landlord can not evict a tenant for non payment of rent unless the rent is at least three months in arears. Correct?

Wrong. Where did you get this piece of misinformation? If you don't pay rent you get evicted after proper notification and court hearing.

In all of the material I have read, it says nothing about a landlord having to carry a tenant for 3 months with no rent. It is my understanding in NYC that a landlord can evict a tenant for non payment of one month's rent.

Landlord's Guide to Eviction in New York City | eHow.com.

I also wonder where you heard this. NYS law allows a THREE day pay or quit notice. If rent is not paid when due, they can serve you a notice to pay or move in 3 business days. If you don't pay, they file for an eviction.

As noted, there is no truth to the three months

Another urban legend shot down at AMHD. LOL :D