Being on the bottom rung, especially as an intern, sucks. If you are getting piled on too much, there is a good chance people are taking advantage of you.

Make a list of all of your workload, and bring it to your supervisor. Tell him or her than you feel burnt out, and you need help prioritizing what needs to get done by when, and what is not realistically not your responsibility. People think this shows weakness, but it actually shows strength to do this.