Dysphagia is a medical term used to describe the problem your wife is having with difficulty swallowing. Hoarseness or only being able to speak in a whisper accompanied by dysphagia after cervical spine surgery suggests some kind of nerve damage. The condition is often temporary but may be permanent.
Some experts suggest the number and kind of problems reported after cervical spine fusion are actually underreported. Researchers studying outcomes of spinal surgery suggest that complications such as your wife experienced occur more often than was previously known.
If you have not reported this condition to her surgeon, you should contact him or her for a consultation and further follow-up.