It's not common in BE
I came across this phrase in The Third Twin by Ken Follett. He's a British author, but the novel is set in the US, and maybe the writer put in this phrase to make it "sound AE":I'd never heard of it before I saw your question and looked it up.
Apparently it's much older that that. We must have taken it over to the other side of the pond. See the origins here (phrases.org.uk).till or until the cows come home, for a long time;
forever:You can keep arguing till the cows come home, but I won't change my mind.
I didn't mean it derived from the British pejorative. As I said, it might derivewhat formerly was a common AE expression certainly doesn't derive from the British pejorative,
Just a guess.from the extreme inconvenience that someone would face if they were pregnant with something as large as a cow.