Object Oriented vs Not jQuery & JS
First of all, maybe you should give the user a way to configure the selector - this gives most applications the chance to go for an id selector, others might want to have a more global or unobstrusive approach - so they can just use a data-selector. 

Your object oriented approach is not following the standard principles for jquery plugins - from what I see there you are using jquery so why not use their plugin techniques then. As the jquery docs have a huge documentation of that, here is just a small example:

$.fn.tabs= function() {
    this.css( "color", "green" );
};

$( "a" ).tabs(); // Makes all the links green.


See http://learn.jquery.com/plugins/basic-plugin-creation/ for a better explanation. This also makes possible what I showed above - let the user decide what selector to use.

For this simple tabs script I don't see any other considerations when it comes to performance.