It is not possible to do with any of the current P&S cameras at normal focus distances. Some depth of field is possible when shooting macro with a long focal length, or focusing just inches from the front element. The 1/2.5", 1/1.8" or even the 1/1.6" sensor sizes are around an order of magnitude smaller in surface area than an APS-C sized sensor used on most DSLR cameras.
I disagree with the bolded part.
The magnitude of "blur" is directly a result of the ratio of the distance to focal point to the distance of background. The greater the ratio of
A to B (refer below), the greater the blur.
Camera |--A--|-----------B-----------|background
subj
Also, if you take into account that infinity for most PnS is from 3 or 5 meters..
In that respect, you can safely assume that max A+B distance that you can factor in is 3 (or 5) meters, meaning you need to calculate B as (3 (or 5) meters - focal distance A).
Anyway this is the roughest of ideas, given a fixed focal length and a fixed aperture.
With that in mind, the greater the focal length, the greater the "blur".
Bigger the aperture, greater the "blur"
Normal PnS camers are of very short focal length, so it's all about the photographer controlling the distance between the camera to focal point (subject) and subject to background.
If you're limited by focal length/aperture, then you just have to control the distance very carefully.