Arduino struggling to power a large LED strip
WS2812 use around 1mA when they are off. So that's already 400mA with no LED lighted. USB can supply around 500mA. So you only have 100mA available. 

Each led package has three colored leds inside; Red, Green and Blue. Every color will use around 20mA when fully turned on.

So you can only turn on 5 colors at full brightness at 500mA. 

Using a 2.5A supply you could go up to 105 colors, or 35 leds full white. 

This would be more than enough for a word-clock, as most leds will be off.