Remarkably, the law doesn't even require devices to be connected to the Internet. Since 2008, it applies to pretty much everything with a microchip. So if you're visiting a friend and you use his coffeemaker without permission, watch out: You may have committed a federal crime.
Until now, the critical limit on the government's power has been that federal prosecutors rarely charge misdemeanors. They prefer to bring more serious felony charges. That's why the administration's proposal is so dangerous. If exceeding authorized access becomes a felony, prosecutors will become eager to charge it. Abuses are inevitable.
The technical computer security gaps exposed by recent breaches by lulzsec and anonymous are not going to be closed with another round of increased criminal penalties. The APT doesn't care about your sentencing guidelines.