var timeoutId = 0;

$('#my_element').mousedown(function() {
    timeoutId = setTimeout(my_function, 1500);
}).bind('mouseup mouseleave', function() {
    clearTimeout(timeoutId);
});

Feel free to comment if you can add help to this page or point out issues and solutions you have found. I do not provide support on this site, if you need help with a problem head over to stack overflow.