how many days over the given departure date is seen as a violation by immigration officers?

Any time you remain in the country more than authorized results in the accrual of unlawful presence. Accrual of more than 180 days of unlawful presence triggers a bar to future admission. However, a lesser stay can have serious repercussions. You can find yourself denied a visa or entry in the future as a matter of discretion. You should try to depart the country in compliance with your authorized stay. If you cannot do so, request an extension of status. You can read more about visitor visa's at http://myattorneyusa.com/travel-visas.