Hi cnal,
I am not sure if there is a CNA shortage, but I know for sure that there is a shortage of qualified CNA. If you do your homework you won't have a problem to find the job you are looking for. Most CNA start their career in a nursing home because most of the time there is an open position. This is because Nursing homes typically have a high turnover with CNA. Many leave after working there for a short period of time.
Now, in order for you to get the job make sure you present yourself the right way. You are a new-grad, which makes things a bit more difficult. You somehow must show the hiring manager through your resume or when you talk to her in the facility that you are qualified to do the job not only by your certification, but also by your general attitude and if possible experience. Experience really counts. Think of what you have been doing before you became a CNA. Have you taken care of a family member? Worked in healthcare in other areas? Done volunteering work? Etc.
Also, make sure you get your documentation in order before you apply. At minimum you will need your license, CPR card (Amercian Heart Association), resume.
Good luck,
Christian