If you can't find a job you can still build your social work resume with volunteer experience. I've volunteered with a local rape crisis center for the last two years. I take shifts for their helpline. It was only two Saturdays of training. I can take the calls from my cell phone and usually do two - four shifts per month (each 8 hours long, but I've never received more than 4 calls in one shift). It's been a great way to practice some social work skills and it also looks great on my resume, but it's taken minimal time/effort on my part. There are a lot of hotlines that can use volunteers, depending on the population you are interested in working with.
Given your undergraduate background, I think finding different places to volunteer with based on the population you think you want to work with could greatly enhance your resume.
Other places that look good and are usually looking for volunteers - child advocacy centers, shelters (women's shelters, homeless shelters, etc.), food banks, CASA or guardian ad litem (depends on your state), Gilda's club etc.