How do I make a 12 LED grid USB powered?
There's no such thing as a "default type LED". LEDs exist in all shapes and (literally) colors, and it's mainly color which determines the voltage.
If you have a 1.4V LED you can't just put 1.66V on it. Either your LED will die in smoke, or your power supply will cut off (which seems to happen here if I understand correctly).
You need resistors. They will limit the current through your LEDs, you can't do without.  

Calculation of resistor values:
Suppose 1.4V LEDs requiring 20mA. Then 3 LEDs in series will have 4.2V over them, leaving 0.8V for the resistor. \$ \frac{0.8V}{20mA}=40\Omega\$ . Pick the closest E12 value: 39\$\Omega\$.
Power \$P = V \times I = 0.8V \times 20mA = 16mW \mbox{   } \$  ,  so any resistor type will do (even an 01005, if you would feel tempted...).  

If your LEDs' voltage is close to 1.6V the voltage over your resistor is too small for a proper current setting; a small variation in LED voltage will result in a large change in current, and hence brightness. In that case only put 2 LEDs in series.