(Time/CNN/Harris Poll, December 2002)
13% will, 52% won't, 34% world won't end (volunteered)
The surveys agree in finding that a little more than half of Americans believe in the rapture (usually 80-90% of Americans say they are Christians, so 63% of Christians would amount to about half of all Americans). The one exception was the Time survey of 2002, where only 13% said they did. I can think of three explanations for the difference:
1. The Roper Center made a mistake in transcribing the results--the 52% should go with "Yes"
2. "Lifted up" suggests a physical event, while "taken up" seems more general. People may find the idea that believers will be saved more plausible than the idea that they will literally be lifted up to heaven.
3. The 2002 survey refers to "people who God has decided to save," while the others refer to the "religiously faithful." People find the idea that people can earn their way to being saved by being faithful more plausible (or appealing) than the idea that God will just decide.
Explanation #3 appeals to me: it would say something interesting about the contemporary American approach to religion. However, I've learned that when given the choice between a simple-minded explanation like #1 and a subtle and sociologically interesting one like #3, the simple-minded one is usually correct. Stay tuned for further investigation.