National Holidays and Work Exigencies
The national holidays are only on the 15th of August, 26th of January, and 2nd of October, and they have to be necessarily observed as holidays. However, there is a condition: in cases where work exigencies demand it and subject to the provisions of the National Holidays Act applicable to your state, these holidays could be converted into working days.
From your query, it is not possible to discern the state where you are located. Many states like Uttar Pradesh, Kerala, Tamil Nadu, Bihar, Andhra Pradesh, Orissa, Karnataka, etc., have enacted the Industrial Establishment (National & Festival Holidays) Act, and you have to consult the provisions made therein. As a general rule, it can be stated that a person working on such holidays would receive additional payment, an additional holiday, or both. In any case, by putting a condition during the interview that you have to work on the National Holidays of India cannot deprive you of the compensatory arrangement provided in the statute. Upon receiving more details, the matter could be further examined for the legal remedies available.
Regards,
KK