I'm a permanent resident but don't have a CUIL. The missus says it would complicate matters. As I have no desire to become Argentine anyway it doesn't matter .
Don't they automatically give you a DNI when you become a permanent resident? That usually comes with a CUIL. You can look up your CUIL online with your name and ID number.
Also, as far as I know, there is no road to citizenship. I am currently doing the paperwork for my son and my husband. My son is getting citizenship but they told me all they can offer my husband is residency through the "family reunification visa"... I don't know.
Your wife said it would complicate matters to get a CUIL? Or to try to pay taxes?