I really don't see just making the playoffs as a great accomplishment. Making the playoffs in the weak East is nothing special. I am pretty sure the 7-8 seeds (maybe the 6th) will have below .500 records entering the playoffs. Not great.
That being said, winning a 1st-round playoff series would be a great accomplishment. That would be their first since 2005. To do that, the Wizards must grab one of the 3-6 seeds to avoid the Heat or Pacers in the 1st round.
The first 2 games after the Break should be good barometers. They play 2 teams (Raptors, Hawks) they probably will battle for the 3-6 seeds. I did the whole who they should beat on the remaining schedule (at least Vegas would probably give them the odds).
Here are what should be wins: Cleveland (yeah I know they lost before), Orlando (3 times), Philly, Utah, Sacramento, Lakers, Boston (twice, yeah I know they lost before), Milwaukee (twice). Those are 12 very winnable games. Knowing the Wizards, they will find ways to lose 2-4 of those games.
They have good chances of beating other teams like Charlotte, Toronto, Chicago, Hawks, and the Nets. I figure those are who we battle for the 3-8 seeds (with maybe the Knicks making a slight run). They only have a few super teams left on the schedule (Heat twice, Pacers, Blazers).
A final record of 45-37 would easily lock up a 3-6 seed. But the Wizards would have to go 20-10 the final way. Not realistic. Probably 15-15 is realistic so that puts them at 40-42. That probably would be good enough for the 6th or 7th seed. As long as they avoid the Heat or Pacers, I really don't see anybody they can't beat in a 1st-round playoff series (although the Nets are a sleeping giant).
That would be their first playoff series victory since 2005. Wow, almost 9 years. We will see.