It depends on the relative humidity of your house. First thing, turn off the AC, unless it's godawful hot. The AC dries the air, and that means the newts will dehydrate faster.
With reptiles, I'd say to just be patient and they'll turn up, but amphibians are more problematic: they have the reptilian talent for finding hiding places, combined with the problem of dehydration in the arid environment of your home. This boils down to 'find it fast'.
Your species is pretty middle-of-the-road in terms of resistance to dessication; it's not gonna dry up immediately like a hellbender, but it doesn't have a trully terrestrial stage like the eastern newt or plethodontids. It's hard to really estimate how long it'll last, but not more than a few days unless it finds a humid hiding place.
A good trick for finding lost herps is to look at the cage and where it is, then follow the edges of the walls. These animals don't like being out in the open, so they'll tend to stick close to the wall. Look for cool areas, dark area, and wet areas (preferablly areas that are all at once). It might help to put a small plastic box of wet soil or moss down with a hole in the side near the ground; the newts might find this is hide there, safe until you find them. Also, check *inside* the furniture, you'd be amazed the places they can get into.
I hope you find him!
Mokele