First of all, lighting area is determined by canopy area. Its the same as the "footprint" of the grow area; vertical height doesn't "count" here.
So if your box's base is 19x14" (or 1.583 x 1.167 ft) the area you'd need to light is 1.85 square feet, (not 3.25).
If you figure 50 watts per square foot is optimal for HPS lighting, the space you describe would need about 90 watts of HPS. Unfortunately, there is no 90 watt HPS.
150 watts would represent about 65% more light than your plants could use. The extra light won't hurt the plants (and you'd probably see pretty good lower bud development), but you'd be well past the point of diminishing returns on light, so you'd be wasting electricity, and more importantly, adding a lot of unnecessary heat to a really small box probably already prone to overheating. More heat = more cooling necessary and more water lost from the plants via transpiration, meaning a lot more watering.
So I'd suggest just sticking to the 70 watt, and if you feel like your plants aren't bushy enough, you could add in maybe 1-2 more fluorescents for side/supplemental lighting.
Next issue, 21 inches tall is pretty short.
If you're running an HPS you'll need at least 4" for your bulb and reflector, plus some clearance from the plant tops so they don't burn. If you figure your pots will have to be at least 6" tall, well, now you're really down to just under one foot for total plant height.
It can be done, but you will need to stick to short strains, and/or train them carefully so you don't run out of room in growing.