Let's do the math. Uncompressed 1080p RGB frame is about ~6MB big. USB 2.0 can transfer up to 60 MB/s but it works in half duplex so one-way data stream won't exceed 30 MB/s.
It means typical single USB 1080p webcam can provide you 5fps.
There are webcams with hardware H.264 or MJPEG encoders which could provide ~10x more frames, but a) 60fps would be still hard to get even from single webcam and b) it is an open question, whether such hardware can be handled by Pi (http://www.raspberrypi.org/phpBB3/viewtopic.php?f=31&t=28887, https://superuser.com/questions/639703/using-hardware-compression-for-webcam-in-linux).
And even if you manage to get 60fps HD stream from webcam, you probably won't be able to save it anywhere. LAN is too slow (100mbit is about 12 MB/s), class 10 SD card is ~10 MB/s, USB is already saturated in opposite direction, so you won't achive the same speed the other way.
60fps in HD is still domain of dedicated hardware, like GoPro sport cameras.