I made a Litecoin withdrawal to an online merchant. The merchant uses a timer- if the currency is not sent within the alotted time, the transaction is cancelled. Dumb of me, but I sent the coins directly from exchange to merchant. Unfortunately, the withdrawal did not go through automatically, probably because I'm on vacation so this took place from a new IP. I sent a support ticket to hopefully speed up the process. Asked a mod if it's possible to cancel a withdrawal awaiting approval, and it's not (coolio).
Poloniex promises that withdrawals will be manually approved within 24 hours, but I have far less than that time so I'm fairly anxious.
Poloniex has in their terms and conditions that withdrawal is within twenty four hours. When I make my last withdrawal last time it take less than 10 minutes and my wallet was credited. My advise to you is to be patient for the 24 hours to elapsed and if you did not receive your payment then know that something went wrong.