Nail fungus CAN spread to the skin.
More Info: Fungal infections can spread from person to person, to other nails, and even to your skin. 
The most common infection that occurs when a nail infection spreads to the skin is paronychia. Paronychia occurs around the nails as a painful, red, swollen area. The condition is usually not problematic but in rare cases of complication can result in abscess, permanent nail disfigurement, or spread of the infection to the bones, tendons, or bloodstream. [“Paronychia.” National Library of Medicine]
What Is a Fungal Infection?
Fungal infections can be caused by a variety of fungi, but the most common nail fungal infection is caused by Trichophyton mentagrophytes or Trichophyton rubrum the same fungi that causes athlete’s foot. The infection can spread as long as it is present. [“Athlete’s Foot-Cause.” WebMD]
How Do Fungal Infections Spread?
Fungal infections are spread from person to person by direct contact, or by coming in contact with an object that an infected person has used, such as a towel. Warm, moist environments encourage the growth and spread of fungal infections, which is why they are so common in public showers. You can also spread a fungal infection by sharing nail files and clippers.
Review Fungal Infection Prevention
In order to prevent the spread of fungal infections, do not share personal items such as towels, socks, or manicure tools. Never go barefoot in a locker room. Try to keep your feet dry by wearing cotton socks, allowing shoes to fully dry before wearing them again, and allowing your feet to get air periodically throughout the day.
 “Fungal Nail Infections-Topic Overview.” WebMD – Better information. Better health.. N.p., n.d. Web. 7 June 2012. <http://www.webmd.com/healthy-beauty/tc/fungal-nail-infections-topic-overview>.
”Paronychia: MedlinePlus Medical Encyclopedia.” National Library of Medicine – National Institutes of Health. N.p., n.d. Web. 7 June 2012. http://www.nlm.nih.gov/medlineplus/ency/article/001444.htm
”Athlete’s Foot-Cause.” WebMD – Better information. Better health.. N.p., n.d. Web. 7 June 2012. <http://www.webmd.com/skin-problems-and-treatments/tc/athletes-foot-cause>.
“Fungal nail infection: MedlinePlus Medical Encyclopedia.” National Library of Medicine – National Institutes of Health. N.p., n.d. Web. 7 June 2012. http://www.nlm.nih.gov/medlineplus/ency/article/001330.htm
“Fungal infections cause about half of all nail disorders. They are more common in toenails because the toes often are confined to a warm, moist, weight-bearing environment.” Nail Statistics, American Academy of Dermatology