Cyclone Nargis, the cyclone that hit Burma over the weekend, had been tracked for days before it made landfall. The Indian Meteorological Department (IMD) named it a tropical cyclone when it was well east of the Eastern coast of India (on April 28) and by May 1, the tracks all pointed to Burma with peak winds of 100-135 miles per hour. This would have made it a Category 4 hurricane. It was 36 hours after that report that the storm made landfall in Burma.
In other words, there was a specific, hair-raising cyclone warning 36 hours before landfall. Had this been North Carolina or Florida, evacuations would have happened, people would have left the coast and the number of people dead would have been minimal. Louisiana or South Carolina may have been a bit worse, but the majority of inhabitants would have been safe. They would now be going back home to see how much of their homes could be salvaged.
In Burma, more than 20,000 people have died and more than 40,000 more are missing. Burma, obviously, is an extreme case -- it's been under the heel of a military junta for decades. There does not seem to have been any emergency response whatsoever. Had Nargis hit South India, would things have been any better? Knowing what I know about Indian disaster preparedness (I was part of a USAID project to help India build a disaster mitigation program last year), it would have been better than Burma but not as good as any American state.
The problem in India is not the warnings (the IMD identified and tracked Nargis for days before it made landfall) or the dissemination (there's a raucous press and reasonably efficient transmission mechanisms) but the lack of any serious options for the warned. Tell a resident of South India that a cyclone is approaching, and there is precious little that he can do. The road and rail infrastructure is too poor to carry out mass evacuations. And the thatched roof housing that is common in slums and villages is too fragile to withstand cyclone-strength winds.