I've got a shirt on my site. I have a total of 10 in stock, which I've put in the product stock levels.
 
I have 4 options with the following stock levels:
1 medium brown
3 medium gray
4 large gray
 
I have "use stock levels" checked on the product and in options. I just tried adding 6 of the medium brown to my cart and it allowed me to do this. Shouldn't I have gotten an error message saying there's not enough in stock to fulfill this order? Is there some option or setting I'm not aware of that I need to check?

Have you ticked the hide box on the option setting

Yes... this is a big issue. If you have 3 products. and the customer selects 10, it will add them to the cart. it won't hide it because you have 3 of them.
 
I don't want to show my customers my stock availability. I just want it to default to something like back ordered for 3 7 of them.

As far as I can see if you only have 3 left and the client orders 10 because obviously the add to cart button is still present (due to 3 in stock) the system message alerts the client that there is only 3 in stock.
 
This is achieved by ticking the hide box for the option as earlier suggested.
 
Yes I agree Dan if you still want to take an order for the full 10 and backorder 7 there is no in between measure to alert the client that only part of the order is in stock. However it would be clear to clients that there was only 3 in stock if 7 where backordered anyway from a stock level point of view.
 
I personally don't allow backorders and usually have everything in stock so for me personally the system is adequate.

The static message for this message is PRODUCT_LIMIT_MSG

Okay, did that and most of the time it works. Occasionally it's letting me add more than in stock, or using the total item limit for the error. Weird.
 
Also, thanks for the tip on the message, as I needed to rephrase that.