A public option in the United States will never be socialism. A public option is just that, an option. People would still be free to shop around and purchase insurance from private companies. It was always meant to compete with and not replace private insurance companies. The United States Postal service has UPS and FedEx as competition and all three do well.
First and foremost, the term "socialized medicine" is an extorted and misunderstood phrase. Socialization is not something to fear: roadways are an example of socialization. Providing a public option for those who can not afford regular insurance is no different that providing someone the right to an attorney if they can not afford one.