Can your employer make you resign?

I have been at my job 9 months. It is an extremely larger work load than anticipated. I have been writtten up twice. The company has no handbook or contracts. I went to the er on tuesday June 21, 2011, have a letter to go back to work in two days. I went back on Friday. I also worked the next Monday and Tuesday. When I went to work on wednesday I was pulled into a meeting and told I was a hard worker, I did my best but that the work load was too much and they decided to hire an accountant for the position. They told me I could resign and they would pay me an extra month of work or resign and not get paid but that they where not firing me and did not want to pay unemployment. They said they would give me a good reference but I need to give a resignation before they pay me. This place has other issues but I have kept my mouth shut and I don't think you want to read 5 pages. Any answers would be greatly appreciated. I have not submitted a resignation because I liked my job. I even asked them if they could hire someone else to do some of the stuff so the work load was lighter but they said no. What to do?