I agree in general with the above regarding the obligation of a US citizen to pay tax on his or her worldwide income. However, I would add several corrections/comments to the above regarding the foreign income exemption.
1) The Foreign Income Exemption is 92,900 USD, not 80.
2) In addition to that amount, you may be entitled to deduct or exclude certain foreign housing expenses as well as food.
3) You can be entitled to the above if you meet the bonafide residence test or physical presence test in a foreign country and have your tax home in the foreign country.
4) The IRS doesn't go investigating to confirm if you have paid taxes in your foreign country of residence.
Regarding the rest, LostinBa is correct in stating that if you exceed that income threshold, as US resident, you would have to pay taxes on the income earned in Arg as well as paying in the US as there is no treaty. However, I believe you would only pay double on the amount over 92,900 USD.
Example: You earn 100,000 for work performed outside the US. Assuming you meet the requirements, you would be exempt from paying income tax on the first 92,900. The remaining 7,100, USD, you would have to pay federal income tax on. If you are paying income tax in the country of your residence, you would pay the applicable income tax and then on the 7,100, you would have double taxation.
Side note on Argentine income tax which I find interesting (which is far too complicated for me to even attempt to explain - suffice to say, I rely on my accountant here). If your employees make less that 10K pesos a month, the assumption is that the individual will pay and it is up to them to pay their income tax. Once their monthly income exceeds the 10K threshold, the company must withold income tax and pay on the employee's behalf. i guess the gov't is not that confident that the employees would pay?!
