Now, the singer seems obsessed with these 32 footsteps. What, exactly, were these "footsteps"? The song seems to be about a break-up. Did the woman take 32 footsteps when she left, and that was the last he saw of her? Unless she took very large steps, it is likely that she would still have been in his range of vision after taking a mere 32 steps. It has been suggested that the 32 footsteps might represent 32 days (one more than the amount of days in a long month), and a case could be made that they represent 32 months, especially when you consider the "32 new moons" line. Well, whatever they are, they represent the woman's leaving. Now, for the rest of the song.
"32 footsteps leading to the room where the paint doesn't want to dry"
An interpretation at tmbg.org contains the hypothesis that this line refers to a fear of commitment. This might be the case.
"32 footsteps running down the road where the dirt reaches the sky"
This could mean that the woman was past the horizon in 32 steps, but, as I mentioned earlier, this would have required very large steps.
"32 feathers in my brand-new Indian head-dress"
Now, a new idea that I thought of was that the singer is now involved in a new relationship, hence the "brand-new Indian head-dress." There will be more on this later.
I've already mentioned the new moons, and the "bing bang bingalong" stuff doesn't seem to relate to the rest of the song, so I'm going on to the second verse. The collapsing house might well be a symbol of a collapsing relationship. "Night turns to day" could refer to his seeing the truth, as opposed to the 32 lies that his ears never saw.
"32 infantrymen running in place
32 boxcars, all of them have your face"
He's seeing reminders of her everywhere. Why infantrymen and boxcars, I don't know. Maybe he's hanging around an army base.
"What's the reason? Why'd she leave?
Don't you know we're on the eve of
32 footsteps?"
Now, back to the "new relationship" idea. He's afraid that this new relationship will end up like the old one. Hence, they're "on the eve of 32 footsteps." I assume he wants to avoid this, so he's trying to figure out what went wrong with the other one.
Sorry if this sounds a bit incoherent. I'm not always that good at putting my thoughts into an understandable form, and "32 Footsteps" is not that easy to understand, anyway.