Nicole, I am faced with a similiar situation in obtaining experience. I would visit your local city/county and ask them if they need help with research, reports, community meetings, and etc. This would help you create your own internship and allows you to interact with local government. If you have a full-time job and cannot go in during their hours you can try and get them to allow you to work on projects in your free time then email them the completed work.

I currently do the internship work in my free time because I cannot find a full-time job that will allow me to get the experience. This process is slow but it is better than having no experience.

Good luck

Nicole -
David's recommendation is good. There are also entry-level internships/Fellowships nationally that pay, if you are able to relocate. Getting engaged and networking in professional associations like ICMA and your state association are also key. Knowing someone who knows the quality of your work in your profession is critical in getting the job you want, but essential during lean times.
We have an online column called Career Compass that also has some great advice on growing experience and demonstrating value
http://icma.org/en/icma/career_network/career_resources/compass.

If agree with the suggestions made. After I completed my MPA, I worked, for no pay though, at a locality here in VA for a month just to get experience. During that time, the person I worked for called a friend who was looking for an intern, with pay!!, and recommended me. I got the job, which turned into a full time regular position in less than a year, and that's how I broke into local government!

Best of luck to you!