Phht! Just like that.
Actually, according to [The Economist (Dec. 19 2002)]:
To try to understand sleep deprivation, ethical scientists prefer to experiment on rats. In one famous experiment, Allan Rechtschaffen and his colleagues at the University of Chicago placed rats on a turntable above a shallow bath of water. Every time they fell asleep, the turntable started tilting, forcing them to wake up and move to avoid falling into the water. Thus totally sleep-deprived, the rats invariably died within two or three weeks, having first become increasingly debilitated, developed sores, lost weight despite eating more than usual, and suffered a drop in body temperature. If the rats were allowed some non-REM sleep but no REM sleep, they lasted twice as long but still died eventually, after a period of sexual hyperactivity. A control group of rats that were exposed to the same stressful environment on the turntable, but were allowed some sleep of both sorts, survived.
[Another experiment] by Licklider & Bunch did achieve dead rats in "3-14 days", but it didn't say how they kept the rats awake.
See also HumPaper --RichardGarfinkel