I've heard that non residents working in NY more than 14 days are going to be taxed? Is this true? If so, how does that work?

I don't know if you are asking about NYC or NYS - here is the NYS info: Filing Information for New York State nonresidents

I suppose it's possible, but it would hardly be worth the effort to try to collect taxes for income under a MONTH in length for most people.

The threshold is NOT the number of days, but income earned. Professional athletes who come to play in NY state must pay taxes on their salaries for the days they play in New York.

As for NYC, it has been policy to date that only those who LIVE in NYC pay NYC income tax.