Work Wants Me To Resign But Won't Fire Me

This is a crazy post that I never thought I would have to make. For context, I work in Texas and have been working for this small business for 8 months. In those 8 months I have never missed a day of work, taken off, as well as worked through multiple holidays. Well I just got to the point where I feel comfortable buying a house, and requested two days off to close and move. During these two days I have been fully removed from work, and that is where the problem begins. Both days I was off, my boss asked for me to come into work and both days I said I couldn't make it in. Now that I am coming back to work they are saying g that I should have been available and that I need to resign immediately. Here's the kicker; I said no and they have so far not terminated me.

My question here is what do I need to be weary of, and what grounds do I have if they try to do something like demote me or give me a pay cut. Can I simply not sign anything and keep my pay until they decide to terminate me? I know this was a long one so I appreciate anyone who was willing to read this