Target hasn't officially yet commented on the shipping delays. All customers affected appear to have pre-ordered the Series 3 device on or around September 15 (the first date they were available to pre-order), and were subsequently given delivery estimates for today's launch or early next week. One customer has canceled their Target order and ordered the Apple Watch Series 3 from Best Buy, with a delivery estimate of next week on Tuesday, September 26.
Last year both Target and Best Buy delayed the orders of many customers' Apple Watch Series 2 devices, and both companies ended up offering affected users a $50 gift card to use at each respective retailer's physical or online store. If delays are widespread again this year, it's possible that Target will offer some kind of compensation for those suffering from Series 3 delays.
@MacRumors Looks like Target didn’t learn their lesson from Series 2. Bunch of us who preordered Series 3 got delay emails this morning.— Dima Spivak (@dimaspivak) September 22, 2017