Although I have a lot of beliefs in common I don't consider myself part of the reformed theology.  I do believe in Irresistible Grace because I believe in the absolute sovereignty of God.  I can't deny this absolute sovereignty that is spoken of throughout scripture.  I explain it to myself this way (although I admit that I likely don't have perfect understanding.  As the creature, we shouldn't expect to fully understand the Creator.)  Due to the sin of Adam and Eve, we have a sin nature.  That nature causes everyone to reject God.  If we could have true, complete faith we would be accepted by Him, but our sin nature makes this impossible.  When God "calls" or "elects" a person, He unchains them from their sin nature.  Once we are freed from our sin nature, there is no other choice, but to repent and trust Him as Savior because our nature and His nature make it so. 

I'll admit I am still trying to fully understand His sovereignty and our choice.