The last remnant of man's power, man's intellect, man's technology, man's spirit, man's existence on earth, is sputtering into oblivion; the house is on fire and trying to save itself. Like what man has done to himself in his world, the house is what is left of him. Pathetic, helpless, running out of resources, the house that helped sustain human life can no longer sustain itself:

"Fire!" screamed a voice. The house lights flashed, water pumps shot water from the ceilings. But the solvent spread on the linoleum, licking, eating, under the kitchen door, while the voices took it up in chorus: "Fire, fire, fire!"

The house tried to save itself. Doors sprang tightly shut, but the windows were broken by the heat and the wind blew and sucked upon the fire. The house gave ground as the fire in ten billion angry sparks moved with flaming ease from room to room and then up the stairs. While scurrying water rats squeaked from the walls, pistoled their water, and ran for more. And the wall sprays let down showers of mechanical rain.

But too late. Somewhere, sighing, a pump shrugged to a stop. The quenching rain ceased. The reserve water supply which had filled baths and washed dishes for many quiet days was gone.

The house is mankind, the pump is the heart, the water it pumps is blood. All is gone, collapsed upon itself. And nature, finally devoid of its troublesome humans, goes on as usual and without a eulogy.

It is not very clear as to what you are asking.  You are right that there is a line that is similar to the one you cite in the Bradbury story.  The actual line reads "Somewhere, sighing, a pump shrugged to a stop."

The line occurs very close to the end of the story.  What is going on is that the house is finally giving up.  It has been trying to fight the fire that is burning it down, but now it is no longer able to do so.  The reason for this is that all the reserves of water have now been depleted.

Feel free to clarify your question if you wish.