Considering the risks, is it even worth the trouble to keep that germy sponge around? Most kitchen sponges are made of cellulose, an organic compound made from a mixture of wood and cotton fibers. Cellulose is good at soaking up liquid, which is useful for cleaning up spills, but that same property is what makes sponges an excellent refuge for germs. We also use sponges because they're cheap and easy to find (just about every grocery store or neighborhood pharmacy stocks them). But they aren't the only option available.
Dishrags are commonly used to clean dishes and counters, and -- although many of the same studies that have found high levels of bacteria in kitchen sponges also found similarly high levels in dishcloths -- they're generally considered to be slightly less bacteria-filled. For example, a recent New York Times article observed that dishcloths "become saturated with bacteria, although since they dry more quickly than sponges, bacteria are less likely to breed." Dishcloths dry faster because they are thinner and easier to wring out than sponges -- and they'll probably get washed more often to keep them from looking so gross.
For a quick-drying tool, you might be better off moving away from sponges and dishrags and trying something less absorbent. For example, scouring pads (which are often paired with kitchen sponges) effectively remove food from dishes and kitchen surfaces, but they are less absorbent, and as a result, they tend to dry faster. A variety of plastic and synthetic dishwashing tools, like cleaning brushes, are also available at most grocery stores. As with sponges, other types of cleaning tools should be disinfected regularly.
For lots more information about keeping kitchen sponges clean, read on.