The answer is to limit transmit power, but there's some real questions as to the feasibility of this as an approach to learn a language.
The simple answer is that the Americas have radio, but not large power production systems. Consider that a small walkie talkie can operate on a pair of AAs, and a radio reciever can also operate on a pair of AAs. However, the radio station transmitters are measured in megawatts. If such localized power is simply not feasible with the way the American technology progressed, then they can't transmit. Perhaps their society valued efficiency over brute strength.
However, I do have to point out a major hurdle for your idea: the Americans probably can't learn English this way. You can't learn a language passively without some shared context. The only thing they could talk about is the weather, and for the most part the weather is very different half way across the globe. Perhaps the Americans might learn the words for the seasons, because both parties are in the northern hemisphere, but this would probably be the limit.
Consider if you had a message like this:
Uvtu cbjre trarengbef ner znpuvarf.
Now you've spent a great deal of time analyzing this langue. You understand the grammar petty well. You understand that if a sentence has the word "ner" in it, it describes something that has some transitive behaviors. You've seen "Znpuvarf ner gbbyf" and "znpuvarf" is on the right side of "ner" in our sentence, so you think it's highly likely that "Uvtu cbjre trarengbef ner gbbyf" would also be a true sentence. Unfortunately you don't have any context to know for sure.
But how could you possibly know that "znpuvarf" was the word the Europeans used for machines? You never got to see one, and you never got to ask the Europeans questions. You need something like the Rosetta Stone to stand a chance of getting the meanings right.
And I'm being kind here. The sentence structure I used for the language in this example is very similar to English. The meanings of the words are also similar. We don't have issues such as the Chinese word "Ch'i," which is brutal to try to capture in English.
In fact, all I did was rot13 encode English to create that language. If you knew English, and I gave you a large enough text, you'd have eventually realized that all I was doing was letter substititions. However, if you didn't already know English, it would have been inpenetrable.
Languages are designed to be used in a common context, such as face to face communication. It is, in fact, mathematically provable that you cannot determine whether a sentence is true or not by doing nothing more than listen to sentences.
It's not until you're face to face with your newfound friend, and someone does something terribly foolish in a cute sort of way, and that friend points and exclaims "baka!" that you stand a chance of understanding what "baka" means.
(In this case, "baka" is not rot13. It's actually a Japanese word which is terribly frustrating to try to properly translate into English. "Fool" is a decently close word, but it misses out on key nuances)
For a wonderful depiction of what happens when you lack proper context, I highly recommend the movie Galaxy Quest. In it, they have an alien species which passively observed our Star Trek like TV show, and then tried to interact with us based on those observations. Hilarity ensues, and they don't even try to approach this language question. It's the engineering that goes horribly wrong when they build their Star Trek like ship.
Edit Reading the comments has been fascinating. It appears this task is less clearly impossible than I had thought. HAM radio operators demonstrate the ability to connect across the globe with very low power, though such connections are spurious. This suggests that transmission may be possible, but they might not find it valuable because they can't control the environment enough to maintain a reliable connection to one individual over long periods.
The second interesting tidbit was finding out that AIs were having great success in identifying words which have the same semantic meaning in two language without an interactive back-and-forth pattern or parallel sentences.
This would make it possible to identify, for instance, the word for "leaf" and "tree" by using their relationships.
I still believe the Native Americans here could not achieve this. At the very least, it would require a robust computer hardware production capability, which is at odds with the "low power" argument. However, it does show there's a sliver of hope. It's possible, though I'd still argue improbable.
Thanks for the comments, all!
