Low Source Voltage: Driving 2V LED with 1.8V Signal, 5V Supply
The problem is that you're trying to use the N-FET in a high-side source-follower configuration, but without enough voltage drive to accomplish the task. Why? The source will be one gate-source voltage (Vgs) below the gate. Switching FETs have Vgs thresholds of between 1.2 to 4V. Even a low threshold FET like a BSS138 (Vgs=1.3V), the best source voltage you will see is 1.8-1.3=0.5V. Not what you're looking for.
If you add a second N-FET as an inverter / level shifter and use a P-FET on the high side, that will give the desired result. See below.



simulate this circuit &ndash; Schematic created using CircuitLab