Guess the question itself sums it up, Is it feasible? If so, how?
To maximize the background blur, you can do three things:
- increase the aperture
- zoom in to use a long focal length
- shoot something that's close to you
On a compact camera you often won't have direct control over the aperture. You might try to trick it by playing with the scene modes: try portrait or sports (sports mode tries to increase the shutter speed so it'll increase the aperture).
Points 2. and 3. might work against each other: you may not be able to get close with a long focal length because the camera might not be able to focus. So this'll take some experimentation to get right.
To get a strong background blur requires a small depth of field which is hard to achieve on a compact camera due to how small the sensor is. It doesn't give enough space for light passing through the lens to diverge from the focus point.
How to maximize the amount of background blur, however, is no different from on a DSLR. You need to minimize the depth of field which means you want to shoot with the fastest available aperture and longest possible focal length from as close to the subject (and far from the background) as possible.