Monoprice is listing cases for the new iPhone 6 as low as $5.60 with free standard shipping. Choose from several different colors and styles.
These probably aren’t going to be the best case you’ve ever owned, but for less than $6 they should be perfect to hold you over until you can find your ideal case. As of right now, the cases are slated to ship by tomorrow, so you shouldn’t have any problem getting one before September 19th. Note: Monoprice doesn’t mention if any of these cases are compatible with the iPhone 6 Plus.
Another best bet is to pay a couple extra dollars and go with a name brand case (update: buy through the Spigen eBay store to save even more). Either of these options are (probably) a smarter buy than Apple’s newly announced $35 silicone and $45 leather cases.