customs will actually give you more grief is your visa does come thru- that is to say, they care almost not at all about standard 90 day tourist visas, which are issued in ten seconds at the point of entry.
But the exit from the airport, with your 3 suitcases, is different from that- if you are not obviously argentine, they dont even look at your passport.
There are two related, but freestanding systems here- 1 is immigration, which issues visas.
2 is customs, which collects duty.
at EZE, the two are pretty separate, and customs applies to Argentine citizens, not, in practical terms, to US passport holders, unless you have 2 dozen iphones and a half dozen laptops, in which case they may actually wake up as your bags go thru the xray machine.
dont worry about it.
3 bags is nothing.
I have come thru with five before. with 6 foot long 1 foot diameter cardboard tubes, with sewing machines, complete sets of pots and pans, with towels and sheets for a 2 bedroom apt, with stereos, monitors, computers, and arcane devices of all sorts.
If you are not travelling on an Argentine passport, they just dont care, unless you are obviously importing bulk items to resell.