Which of these is correct:
- Global warming is a great threat to us people.
- Global warming is a great threat to we people.
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Global warming is a great threat to us people.
Global warming is a great threat to we people.
The first version (#1) is grammatical in today's standard English.
The second version (#2) seems to be ungrammatical (that is, unacceptable), because the word "we" is in nominative case instead of the expected accusative case. The rest of this post will be about version #1.
In your version #1, the word "us" is a personal determinative.
The expression inside the brackets is a noun phrase (NP). The head of that NP is the noun "people". The word "us" is the determiner of that NP.
Here are some similar examples that use personal determinatives, from CGEL page 374:
[5.i] [We supporters of a federal Europe] will eventually win the argument.
[5.ii] [You students] should form a society.
In those examples, the "We" and "You" are personal determinatives functioning as determiners (though they are in nominative case instead of accusative case that is in your example). Those determinatives are functioning as determiners within the subject NPs.
CGEL says on page 374:
Note that CGEL is the 2002 reference grammar by Huddleston and Pullum et al., The Cambridge Grammar of the English Language (CGEL). Related info is in CGEL, "7.2 The personal determinatives we and you", page 374.
Global warming is a great threat to us people is correct; however, as Jason said, you could go without using the word "people."
The reason for this is because "US" is the object of the sentence, and therefore you need an objective case pronoun (ex: me, you, him/her/it, us, you, them). "We" is used for the nominative case (or when it is the subject of a sentence).
"Global warming is a great threat to us people." is more grammatically correct. However, this doesn't mean it is grammatically correct.
Think about the sentence without the word "people."
Global warming is a great threat to us.
Global warming is a great threat to we.
It's obvious which one sounds strange.
Omitting the word before "people" might be a better choice.