Here is a quick snippet how to test if overflow is happening in a DOM element, shamelessly taken from http://www.bramstein.com/projects/text-overflow/.

gistfile1.js

// Check if overflow happens for a given jquery element
function check_overflow(element) {
    var element_clone = element.clone();
    
    element.after(element_clone.hide().css({
        'position': 'absolute',
        'width': 'auto',
        'overflow': 'visible',
        'max-width': 'inherit'
    }));

    var has_overflow = element_clone.width() > element.width();
    
    element_clone.remove();
    return has_overflow;
}