I spent all my 40 votes today and didn't get the "Vox Populi" badge awarded :(
Is this a bug or did I do something wrong? Any other possible reasons?
Many badges don't get awarded the very moment you meet their criteria. Instead, they get checked and awarded periodically by scripts that run every few minutes or hours (sometimes lots of hours), according to how server-intensive the badge is to check for, and how often people get it.
You'll probably get the badge later today. If you don't get it for a whole day, then there's an issue.