The "Top Kill" procedure got going a few hours ago and involves pumping thousands of pounds of fluids into a five-story stack of pipes. It could take several days before they can figure out whether it's able to stop the oil. From the NYT:
The consequences for BP are profound: A successful capping of the leaking well could finally begin to mend the company's brittle image after weeks of failed efforts, and perhaps limit the damage to wildlife and marine life from reaching catastrophic levels. A failure could mean several months more of leaking oil, devastating economic and environmental impacts across the gulf region, and mounting financial liabilities for the company. BP has already spent an estimated $760 million in fighting the spill, and two relief wells it is drilling as a last resort to seal the well may not be completed until August.