Although humans develop technological advancements to make life better, science fiction writers often suppose a future in which technology spells the end of humanity. This is the case in this story. When the story begins, humans have been destroyed by a nuclear explosion. The only things that remain are stray animals and the now pointless technological marvels such as the seemingly efficient house.
The setting is in the future and technology has caused more harm than good. This has become fairly common in some science fiction texts and films. Consider films such as The Terminator and The Matrix; machines have taken over the world. Now, this is not exactly the case in "There Will Come Soft Rains" but the technology humans have created (atomic bombs) has eventually led to their destruction. So, the premise is the same: humans seek advanced technology and, eventually, that technology becomes too powerful for them to stop, control, or use responsibly.
One could argue that it is not simply an indictment of technology; it is an indictment about the irresponsible use of technology. When humans get to a point in which technology does everything for them, they become more like machines and technology (i.e., the house) becomes more human.
"Today is August 4, 2026," said a second voice from the kitchen ceiling, "in the city of Allendale, California." It repeated the date three times for memory's sake. "Today is Mr. Featherston's birthday. Today is the anniversary of Tilita's marriage. Insurance is payable, as are the water, gas, and light bills."
It is as if the house is programming the humans, rather than the other way around. Once humans reach such a threshold (when the machines act more human than we do), we lose our sense of humanity . . . and our faculties of thinking for ourselves. Such a future implies a human population that is thoughtless and without humanity; a good recipe for allowing an event like a nuclear holocaust to happen. Bradbury was certainly a fan of technology. However, he saw the dangers of using it irresponsibly. And this has to do with all aspects of life; not just the production of deadly weapons. (Consider a future - and similarities to the present now - when a person doesn't have to remember birthdays, poetry, mathematics, when to feed their children, how to speak to a loved one, etc. At that point, humanity becomes more like thoughtless, passive machines and this is a dangerous scenario.)
This story gets its title from the poem by Sara Teasdale. In the story, the "house" recites this poem at the appointed time. The poem is equally, if not more, foreboding as it suggests that the world (birds, trees, frogs) will not miss a beat if humans wipe themselves out.