When is a big asteroid next predicted to hit earth?

We don't know when the next big asteroid strike on earth will be. But we are sure it will happen. Sooner or later. There will always be a number of predictions out there as regards when we'll get hit again, but until you hear it from a group of astronomers who have done their homework, it would be wise not to worry too much about it. Oh, and those "seers" who say one is coming? They'll be passing the hat or otherwise expecting payment. Little rocks from space hit the earth all the time. But the history of the earth clearly shows that every once in a while, a very large rock from space slams into us. The damage is so great that large numbers of individual plants and animals are wiped out. Additionally, whole groups of species are killed off indirectly in the aftermath of the collision, and this owing to the damage to the biosphere the blast causes. We think the dinosaurs were terminated as a result of the effects of such a blast. We are starting to look for these near earth objects now. We've got extra eyes on the skys to see if we can spot them. We're crunching numbers all the time on rocks we spot to see if any are coming uncomfortably close. But we haven't seen the next big one with our name on it. Yet.
In fact, many asteroids hit the earth every year!

Most of them are small enough to burn up in the atmosphere though, and the few that reach the surface are too small to cause significant damage so there is no reason to worry.

Big asteroids that can significantly damage our environment or kill many people, plants and animals do hit the planet from time to time, but the chances that we would not see it coming many years before and send up a rocket to "nudge it out of the way" are really really low.
No, ateroids will hit earth when toilets fly!