What happens if you feed 3.3V to a 5 to 3.3 voltage regulator?
The critical parameter is drop-out voltage, which I'll call \$V_{do}\$, listed in your datasheet on page 3.

The output voltage will generally not be more than \$V_{in}-V_{do}\$. (Obviously this breaks down when \$V_{in}\$ is very low. If \$V_{in}&lt;V_{do}\$, for example, all bets are off)

For the AMS1117-3.3, the drop-out voltage is listed as 1.1 (typ) to 1.3 (max) volts. That means to be sure of getting 3.3 V out, you need to provide at least 4.6 V in. 

And if you provide only 3.3 V in, you shouldn't expect more than 2 V out. In fact, that far below the nominal input voltage you shouldn't count on the listed drop-out voltage applying, so you can't even be sure of getting 2 V out.