You still need to expose your photograph correctly. So if you're taking a panning photograph in bright light you have to either use a very narrow aperture or a filter, or both. Of course with a P&S camera, both those are difficult: you may have no control over the aperture at all, and there may be no easy way to attach a filter. If that's the case, you'll have to take your panning photographs in darker lighting.
You don't need ultra-long shutter speeds like 4 seconds, though: my picture here was only 1/15 of a second. If you are closer to your subject and it's moving faster, you can probably get away with an even faster shutter speed.
One thing you could try, although I've never tried this and it may be too awkward to pan steadily, is hold your sunglasses in front of the lens as you pan, as a makeshift neutral density filter.
Finally, if you try taking panning photographs in darker light in order to achieve the longer shutter speeds, your camera will probably increase its ISO to prevent camera shake, which is the opposite of what you want (since panning is, in one sense, controlled camera shake). If your camera has a mode that lets you force the ISO to its lowest value, you probably want to use that mode.
Of course, I hope you've also read this answer -- maybe all you need to do with your camera is leave it in Auto mode, zoom in as far as you can, and take pictures of nearby, fast-moving objects.