Can my employer force me to resign by saying that if I refuse, I will be fired?
Well, your employer can’t weasel you out of unemployment benefits by doing so. According to the regulations governing unemployment benefits in Connecticut, the DOL may not find that you “left suitable work voluntarily” (i.e., up and quit) if you “left work as a result of a demand by [your] employer to either quit or be discharged.”
There are advantages to this situation, for example, you will be able to tell your next employer that you quit instead of having to say that you were fired. But, if you are truly forced to make the choice, you should still be able to collect unemployment benefits.