I have the exact same problem. No screen protector here. It just seems like the proximity sensor is too slow. My original droid had the opposite problem where it would blank the screen as soon as a call was placed and I would have to wave it around or hit the power button to wake it up. Both issues are super annoying.
I just found out why this is. The GNexus requires the phone to be upright before the proximity sensor will turn off the display. If it is laying flat, it won't work. Because of the complexity (the requirement to satisfy both conditions), it seems to react slower.
The hardware itself isn't the problem. It's the stock dialer.
To demonstrate, I made a video. I used the stock dialer and GrooVe IP (a dialer I use for Google Voice). GrooVe IP turns off the screen right away when I put my hand over the proximity sensor. Also, it does not cause accidental ear dialing.
I hope Google will fix this in the next update. It's certainly by design (a bad decision), and can be fixed by software.
Try putting the top (earpiece) edge of the phone to your ear first, then pivoting along that edge to bring the mic toward your face. Sounds more complicated (and slower) than it is, but allows you to hear the earpiece immediately while also getting the sensor close to your face before your cheek hits the touchscreen. I got used to this approach pretty quickly and haven't done any accidental keypad pressing in a while.