These are pressurized light water reactors (PLWR) meaning that they operate under near-critical conditions: if water phase separates into steam and liquid, the heat transfer becomes inefficient and the fuel rods overheat. When the pumps lost power and failed, the engineers let the seawater into the reactor vessel; at this point the core was already partially exposed and melted.
If there is no pressure, steam bubbles are formed near hot surfaces, reducing the heat transfer, so cooling is very inefficient. Overheated zirc casings and fission products (which include platiunum group catalysts) begin to react with water producing hydrogen. The excess steam and this hydrogen need be purged, hence the release of radioactive vapor containing iodine and xenon and high probability of explosion in the enclosure (into which the steam is vented). Because the explosion destroyed most of the control equipment mounted at the top of the reactor (relief valves, etc.) nearly all they can do is adding more (hopefully, fresh) water and (I hope) relieve the excess pressure (it is possible that it is constantly venting, i.e., they lost this last control, too). In the Three Mile Island accident the controls were not damaged.
Steam bubbles + inefficient cooling + release of pressure due to a stuck valve for less than two hours (!) is what led to core melting in the Three Mile Island accident in 1979. If the high pressure cannot be restored, pumping hot water would be impossible even if the pumps are operational, because it will turn into steam in the pump heads and destroy the pumps (that happened, too, in 1979, and they needed to shut down the pumps after losing pressure). If the core overheats, the zirc cracks and the oxide pellets drop to the bottom of the vessel and melt, forming the "corium". The contact with static, low pressure water does not cool this lava too well (because the coolant is isolated by steam) and the danger of melting through the bottom of the containment vessel is quite real. All controls have been destroyed and rebuilding these controls means human sacrifice, as the radiation is very strong. They can only add more water and let the steam out. There is enough heat from the decaying radionuclides to keep it boiling for months if not years.
I do not think the evacuated people will return anytime soon, and they should be happy to be alive and well. This will continue over many months. The art of PLWR operation is that cooling should never be interrupted; there are layers of engineering controls and backup systems preventing this from happening. When the unthinkable happens, little can be done. I am amazed by the "optimistic spin" given to these events in the media. So far, it went from bad to worse. The dimension of the problem is not sinking in.