What does it mean by: This might take a while?
Whether "let's sit here for a while" is short or long is really anyone's guess. It's not implicit in the phrase itself. It could be two minutes or two hours.
That "this might take a while" means "...a while longer than you would probably otherwise expect" is just one of those things. There's no real logic to it.
It reminds me of "that's okay" meaning "no, thank you," which seems to be counterintuitive to many non-native speakers.