So what happens now? Firstly, you can still enjoy them for at least a few days, perhaps longer. You don't have to see them today to enjoy them in all their glory, and as they turn pink in the next few days you can argue that they'll look even prettier.
As they move beyond peak they start becoming more fragile. In ideal conditions (cool, calm, dry) they can hang around for a week or more. In less than ideal conditions (rainy, windy, stormy, warm) they can be chased away sooner, perhaps in as little as 3-5 days. Right now, the weather forecasts aren't for ideal conditions. You can get some sense of what to expect, and the large variation, from this photo timeline.
Want to Help Support DC's Cherry Trees?
If you'd like to help support the care and upkeep of the cherry trees around the Tidal Basin, the Trust for The National Mall has launched an Endow a Cherry Tree Campaign. Donations go to the official Cherry Tree Endowment, which will give the National Park Service additional resources to fund the care, maintenance, and possible replacement of the cherry trees. You can find more information here.
The Trust is dedicated to marshaling private support for maintaining and improving the history National Mall area. I'm not affiliated with the Trust--just an admirer of their efforts.