How bad does your neck/spine injury have to be to require surgery?

Bad enough. . . . If you have a diagnosis that clearly explains the source of your pain, then the decision for surgery depends on how bad the pain is versus how risky the surgery might be. The most important part is to be as sure as possible you have the right diagnosis and that the surgery is as safe as possible. When the disability is bad enough to significantly affect your life, you're ready.
It Depends. After a spine injury, surgery can be an option if the spine is rendered unstable or if there is a pinched nerve or spinal cord. Xrays and cat scan can detect most surgically significant spinal instabilities, while an MRI is the best test to evaluate the status of the neural elements within the spine.
Last resort. Generally, spine surgery is performed in patients with definite abnormalities on imaging which cause persistent symptoms not helped by conservative treatment such as physical therapy and/or injections. Sometimes an acute injury to the spine can make it unstable, or acutely compress the nerve roots and/or spindl cord. In those cases surgery would be performed sooner.