How much is short hair on a girl a deal breaker?

Ok so how much does having short hair really reduce attractiveness or ruin a girls chances of getting a man? I mean many men like long hair but is hair style an extreme preference as in its one of the deciding factors or is just a slight preference? If a girl with short hair aproached you would you feel you were out of her league? Heres the type of short that im talking about, actually post a pic of the kind of short hair you might find attractive...

Put the internet to work for you. via Personal Recipe 2629979