Transfer Characteristics of an EMOSFET
The necessary condition for an NMOS to be in saturation region is:
VDS > VGS - VTH
or VDS + VTH > VGS

You can see the catch here. If you get your VGS too high, you will be in triode region.

I remember a problem in "Design of analog CMOS integrated circuits" by Behzad Razavi, in which he asks how transfer characteristics will change if VDS is low. Give it a read.