I will be honest, I know very little about the internals of git.
I have staged and commit a 40mb directory, but when I come to push...
$ git push --v
If you found this site because of BitBucket failing with that error message, then check out the answers to this one:
Particularly the comment by Nicholas Pickering and Simon Tewsi about exactly what part of the key needs to be pasted into the BitBucket dialog.