Ahead of the launch, Target also opened a temporary store in Manhattan at the start of New York Fashion Week last Thursday. But the colorful shop, which spanned six city blocks, was supposed to stay open for three days, but winded up closing after six hours because items sold out.

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Online, shoppers rushed to the site for the 6 a.m. launch. But soon after, online consumes came face-to- face with its mascot bulldog along with the disappointing news: "Woof! We are suddenly extremely popular. You may not be able to access our site momentarily due to unusually high traffic. Please stay here and we'll try to get you in as soon as we can!"

Even celebrities were tweeting about the launch. Actress Busy Phillips, who plays Laura in ABC's "Cougar Town," tweeted: "Got the bike. Not the colorful one but still SO EXCITED."

Target had planned to continue selling the line into October at all 1,700 stores around the country. But shoppers will be lucky if they can find something they want. In fact, based on a spot check by Target of stores in Minneapolis area, everything had sold out by Tuesday morning. Target is replenishing some merchandise over the next few days, but it will trickle in.

Some shoppers already are trying to capitalize on the fleeting nature of the Target's Missoni collection. As of Tuesday afternoon, there were 1,591 listings for Missoni for Target on eBay.com that were selling for more than double the price found at the discounter. Travel totes were going for $169, while shoes were selling for $129.99.