Singleton Connection Pattern for a Social Networking Site, Multiple Users

I have been reading about Singleton, and i managed to create a Connection Manager Class in PHP that uses a singleton, this enables my program/application to connect to the database, but i want to know since singleton connection pattern has one instance does this affect multiple users accessing the database at the same time. Say for a social networking site with large amount of traffic everyday, will there be connection issues due to large access by multiple users since all will be going through this one instance of connection, wont it also slow down the application?