That one always gets me. The phrase means that the person is wrong about something, and circumstances will compel them to reconsider their position or opinion. The word "think" refers to a cognitive process, such as reconsidering their position or opinion. As for the alternative, what's the "thing" that's coming? Their latest Amazon order is out for delivery?
After a cursory search it seems like both are acceptable. "Think" appears to be the original phrase, but "thing" is more common today, especially in America.