Both my parents and I live in Illinois. I am the only child. They are stubborn and resistant to making a will. They think they don't need one since I am their only child. I have tried to explain to them the advantages of a will without success. They are now in their late 70's with property in 2-states and moderate financial assets. I hope they spend every penny they have earned prior to this time but that is unlikely. What happens and what will I be left to untangle when the day comes

In Illinois if one of your parents dies intestate (without a will) then that person's property is split half to the surviving spouse and half to you as the only child. So tell your mother that if your father dies she will not automatically have his assets to live on. I assume you are over 18 - if not, then it gets more complicated as the probate court would have to administer your half of the property until you reach 18. Finally, if your father dies and you mother acts as executor she will be required to purchase a surety bond equal to 1.5 times the value of your father's estate. Usually when writing a will one includes a clause waiving this requirement if one's spouse or other family member is to be the executor.

Here's an interesting summary:
Last Will and Testament of Illinois Resident Who dies intestate