I love Washington DC in the spring! The cherry blossoms are very hit or miss. Last year we went to see them the very beginning or April (1st, I think) and they weren't quite out yet. We went back down a week later (8th I think) and they were in full bloom. They are worth the crowds for sure. The first time there (when they weren't quite in bloom yet) we stayed in DC for the day, went to see the Mickey statues that were being displayed, went to a museum, and ate lunch at the Old Post Office and it wasn't overly crowded. And that was one of our Spring Break days.
As for the weather, like has been mentioned, it really varies. Last year was chilly, but it can be hot. We were in NYC for part of our spring break last year (very end of March) and we froze--needed winter coats and gloves. I don't know if DC was quite that cold, but it can be. So far this year we've had warm weather so maybe that trend will continue.