Just to show how complex an issue it can be, although the amount of text quoted can be a factor in whether something is fair use or infringement, it's possible for reproducing an entire article to be fair use, and also for a single sentence to be copyright infringement.
So what's the character of the quotes in question? In each case the text is provided for purposes of criticism. Ironically this is one of the clearer areas of fair use, and it seems obvious to nearly every observer that the AP has overstepped their bounds in sending the takedown notices.
But the question is a lot bigger than what happens on a single website. As the AP is finding out now there are some issues that seem nearly universal, not just among bloggers but in the general population. The right to present a text for basic commentary is one of them. It's done in blogs and on discussion boards and forums every day.
As public sentiment has clearly been against the AP they've attempted some damage control, even going so far as to volunteer to write their own guidelines for how articles can be used by bloggers and others. Unfortunately this strategy has two problems. The most obvious is that they don't control fair use. Obviously if copyright holders got to decide what constitues fair use it would all but cease to exist.
But a bigger problem has developed, and it may prove more dangerous for the Associated Press. A number of bloggers have announced that they'll stop using AP sources altogether, while others say they'll only use them as a last resort.The AP may get what they want, but to what purpose and what end result? How much traffic is generated by the links back to AP articles from bloggers, forum posters, and the like?
We may be about to find out, and it's likely to be an answer the people in charge at the Associated Press don't like.