I'm pretty sure that the Oregon Scientfic clocks receive the NIST LW transmissions, which on a good day might get a lot further from Fort Collins than the borders of the USA, but are very unliely to reach you in Argentina.

OTOH, if they use the SW service then you might stand an outside chance.

Lots of info on wikipedia - eg http://en.wikipedia.org/wiki/WWVB

The bigger issue with GPS is power consumption. A well designed LW receiver draws a fraction of the paower of a GPS receiver, and should be able to sync in a fraction of the time it would take GPS to get enough of a lock indoors.

A better bet would be to make a clock that could sync to Bluetooth and have your cellphone transmit the time over Bluetooth every now and again (simple software download should be all that would be required).