I have seen tires come almost completely off a rim before, leaving the tube bulging desparately but not bursting. It's rare, but it happens - although usually only on the way to a full blast of exploding tube seconds later.
As others have said, remove the tire and re-seat, double checking the whole circumference on both sides for tube trapped under the bead of the tire, then inflate. Also check that the tire is seated evenly all the way 'round, and that the bead is not much deeper in some spots than others, as this usually indicates that the bead is much shallower in other spots.