Can I get a round trip non stop flight each way from washington dc to
las vegas on march 10 returning march 12 for less that $200?

Once you go through the 2 week window your options plummet. You might
cross your fingers and pray for a last minute deal but with traveling
on a weekend, you were behind the 8-ball from the start.

Southwest has a very limited number of roughly $200 RT seats in this
market (from BWI) but they sell ridiculously fast.

If possible, it could be cheaper to buy a roundtrip ticket in DC with
the return flight open, and then do the same in Las Vegas, foregoing
use of the return flights, but it may be difficult to book the return
flight at short notice, but maybe you can also do that in advance.
Of course, then, it is tempting to use the open return flights for another trip.

Unfortunately the cheap airline from DC to Vegas is now bankrupt. 
Fly-I (Independance Air) flew me round trip for $160 to Vegas over
Christmas, and that seemed to be the going price for about any
timeframe.  Now that they are bankrupt, you're probably looking at
$250+ for the round trip.

...and people wonder why airlines, overall, never make money.