Hopefully this will give you some hope. I, too, applied w/ Target around Nov last year. Money was tight (after buying a new house a few months prior), and I wanted to get my wife SOMETHING for Christmas (I know, the WRONG reason to get a card is to go from no money to being in debt, but I had a very sizable chunk of money coming in just after the first...$50 on a card was a drop in the bucket).
At any rate, I got the card (don't remember if it was instant or not) at a $200 limit. A couple of weeks later, I got her something around $35, then paid it off a couple of days later. As I started learning about inquiries, age of accounts, etc, I started kicking myself in the butt, because in the last 24 months, I've had 24 inquiries, and because of the late start of my 'credit education', the age of my accounts is somewhere around....oh, 18 months or so, on average. So, angry at Target for giving me nothing but a crappy limit with a bad rate to go with a new inquiry and TL, I put it in a drawer. After the new year, never needed the credit, so it's collected dust. Until now.
I received a letter saying 'thank you for being a great customer, (WTH, right? I only used it ONCE!), you have been upgraded to a Target Visa'. My other CL's are $300, $400, $750, and $2000 (recent CLI, I was juiced!). Well, thanks to my ignorance of all things Target, apparently, I was awarded a $10,000 credit limit. Needless to say, it blew my mind. This was no pre-approval, it was approved, straight up w/o further hard inquiries. I got the card today. SO!
Moral of the story - if they give you a $200 limit, don't fret. They apparently like to take their time, but in the end they make it worth it.
I hope these words give you hope!