Amazon.com (Nasdaq: AMZN) is taking on more than its servers can chew today.

The leading online retailer is selling copies of Lady Gaga's brand new Born This Way CD for a mere $0.99 today, a fraction of the $11.99 that larger rival Apple (Nasdaq: AAPL) is asking for through iTunes.

Amazon's timing for the deeply discounted digital album couldn't be better. Lady Gaga recently became the first Twitter user to surpass 10 million followers. She also is coming off a multi-faceted performance during this weekend's Saturday Night Live season finale.

This promotion also comes just weeks after Amazon launched its new digital music locker service, and a single MP3 album purchase ups the storage capacity from 5 gigs to a full 20 gigabytes.

Unfortunately, Amazon's cloud is bursting under pressure.

Amazon's product page for the 14-track digital CD and booklet is filling up with customer complaints. The most popular problem is that of partial downloads, something that is likely the result of orders hammering Amazon's platform. This is an embarrassing development for the e-tailer, especially since it markets the uptime of its cloud services to enterprises.

It's not just online retailers that are hoping to milk some marketing magic off Lady Gaga's latest release. Best Buy (NYSE: BBY) is selling the physical CD for a mere $7.99, and giving it away to new mobile customers inking two-year contracts. Zynga made a splash with a Lady Gaga social gaming promotion this month.

Amazon better make a quick recovery here, since it's obviously willing to take a big financial hit in offering the MP3 album at $0.99. Ideally, this would have been -- and could very well still be -- a great way to reach out to iTunes loyalists and music fans that aren't familiar with its growing digital media storefront.

A first impression like this, though, isn't going to help the prospects of both its media store and its cloud-based streaming service. There's a fine line between Born This Way and died this way.

Have you downloaded Lady Gaga through Amazon.com today? Share your thoughts in the comment box at the bottom of this queue.

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Longtime Fool contributor Rick Munarriz has made a few purchases through Amazon's digital music store in the past. He does not own shares in any of the stocks in this story. He is part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early.