Yes, but there is a lot of opportunity, a great need, and it depends at what level you are referring.
If you want to be a veterinarian, getting into vet school is pretty tough. Only 10% of the people who apply to any one school get accepted. Once you become a veterinarian, you will need to decide if you want to specialize, which may require extra training called a residency. Residency program are also very competitive. But there is a great need for veterinarians, especially in large animal medicine (food animals and horses), in poultry, and in research.
If you are thinking of being a veterinary technician, this is a little less competitive. Most states have veterinary technician programs associated with state school and community colleges. Here again the need is great, every veterinarian I know is looking for a smart, dedicated, responsible vet technician.