I found this old question in SE-ELL, particularly the comments on the last (Hector von's) answer, and it stirred my curiosity about the usage of object pronouns in subject position.
I believe that in colloquial English, sentences like these can be used:
Us cartographers can map the world / Me and Jeremy are going to the supermarket
But I would like to focus on the following examples:
- In spite of his being a mere boy, he offered to fight the giant
- In spite of him being a mere boy, he offered to fight the giant
- In spite of he being a mere boy, he offered to fight the giant
And
- Our having to undergo this disgrace is a pity
- Us having to undergo this disgrace is a pity
- We having to undergo this disgrace is a pity
For both examples, I would say that (1) is the correct and recommended form, (2) is an accepted colloquialism and (3) is incorrect, but I cannot explain why and especially why (2) must be chosen over (3).