There are many passages in the Bible that indicate that the authors saw the apocalypse as coming in the very near future. One of the most blatant is the First Epistle of John, 1 John 2:18:
This is... difficult to reconcile with the continuing existence of the Earth and human civilisation.
Especially given that infallibilists see the entire world (or at any rate, the human species) as about 6,000 years old, the 1,900 years or so that have elapsed since that was written can hardly be described as a mere hour. It would be almost a third of human history.
Other verses one could point to are Luke 9:27, Hebrews 1:2, James 5:8, and 1 Peter 4:7. The last of these is particularly bad:
It's really hard to see this as foretelling anything other than an imminent apocalypse. Even if "an hour" meant 1,900 years, this verse from Peter uses no such metaphors.