Amazon is not that big of a competitor to Target. The only areas that Amazon really beats Target would be electronics and entertainment. You don't buy clothes from Amazon. You don't buy household supplies from Amazon. And you certainly don't buy food.
If this is a gut-check reaction to Amazon hurting our electronics and entertainment sales, it's several years late. Target has no presence in the digital market except for the fact that they sell the devices necessary to access such a marketplace. This is where the niche should be, because the one thing that Target and other physical retailers have over Amazon is the ability to give consumers convenient access to try before they buy.
They actually are a pretty big competitor in the sense of ease it is to shop online. The try before you buy logic can actually HURT Target and Best Buy down the road. Sure, I'll head over to Best Buy where they have tons of TV's on display, find out which one I like the best, and head online to purchase something that will be free of sales tax, and ship to my door for free in 3-5 days.
According to my DTL, Amazon is moving up the ranks and will overtake Wal-Mart shortly with being Target's #1 competitor. MobileShop (I think is what it's going to be called...) is going to be Target's way of trying to compete with online shopping, but we still are losing tons of money simply from the fact that buying online is often times cheaper.
Just my two cents! Cheers!