My question involves labor and employment law for the state of: San Antonio, Texas

I have worked for my employer for going on two years. They now are talking about training me for a half time manager position. I'm not interested in taking on this role, since it will be ALLOT more responsibilities that I don't want nor need. Can I quit or can they fire me if I refuse to take on this responsibility?

And if I quit since they are kind of forcing me to change my position & my responsibilities, would I then be able to file for un-employment?