I've casted 40 votes on last saturday, and I didn't receive Vox Populi.
How is this possible? I've received the warning I couldn't cast any vote for the next 10 hours that saturday.
We cannot view your voting page to corroborate your voting numbers - Mods cannot easily see how many times you voted, and certainly not who you voted for. Once it's more than a day old, the best we can do is see how times you have voted in the current week/month.
In this instance checking your profile page suggests you have made 27 votes this week, but it sounds as though your voting spree took place last week. Your monthly figure of 127 votes suggests you have made enough votes to potentially receive the badge, but does not confirm that 40 of them were made on the same day.
If you can take a proper look at your own personal voting page at here and count that you definitely made 40 in 1 day, then we can perhaps look into it as a bug etc, but there's not a lot else we can do to explain why you have not received the badge although it is possible that a vote you cast was essentially "voided" if the post it was one was subsequently removed before the daily badge run completed.