You have to have paid the overstay to checkin (though sometimes the checkin clerks do not notice it, and it is only caught before customs, then you have to exit internationbal area to pay and then come back)). Therefore, pay the fine before lining up to check in, or you will have to line up again.
Many people have missed hteir flights because they have failed to do this, with all the attendant huge extra costs and headaches involved.
I would allow an extra hour at EZE incase its really busy.
A year ago when i had to pay the fine, it was 300 peso's, and they would only accept cash.
So i went to the immigration counter (the checking staff will tell you where to go), got the form, went to the ATM and withdrew 300 pesos, then paid at Banco National at the Airport using the form from immigrations, get the receipt, then take that to the immigration counter again, who then stamp it, and you then present it when you leave at immigration control.
You have to go to costum desk in terminal A before you check in(it's in the back at the right side of the terminal). There might be a line. Then you must pay 300$ in the bank next to the custom desk and go back to custom desk with the receipt.
For us it went quite fast, except from the fact that our plane left from terminal C so we had to walk 15 minutes to get there
I would pay in pesos, in cash. Last time I had to pay an overstay fee I was given two prices... one in pesos, the other in dollars. The peso fee was slightly cheaper given the conversion (I think it was 300 pesos or 100 dollars.) I'm not sure if that's changed.
They DO NOT take credit cards. You must pay in cash. Further advice, bring cash with you. A friend of mine missed her fight as she assumed she could pay with a credit card. She couldn't and the ATMs at the airport were without cash (which does happen). She wasn't allowed to get on the plane and had to rebook for the next day.
If you are flying on a Thurs/Fri/Sat, there is usually a longer line. Ditto on if you are flying out between 7 PM and 11 PM when most of the international flights leave. I would guess that an hour is safe.