Is there a big demand for veterinarians?

This depends upon what you mean by "big demand". Overall there is moderate demand for veterinarians in private practice; in rural areas there are unmet needs for large animal and production veterinarians, although there is not enough work to support a full-time veterinarian in these areas. In food safety and public health there is a major need for veterinarians, although most employers don't recognize that they could use veterinarians to fill their vacancies.