use keyup instead of keypress. just tried it and it worked better.
$('#txtbox').keyup(function() {
var textLen = $(this).val().length;
var textLeft = parseInt($(this).attr("maxlength")) - textLen;
$('#charCount').text(
textLeft + ' character' + (textLeft == 1 ? '' : 's') + ' left'
);
});
$('#txtbox').keyup();
I added the maxlength attibute to your textbox and just grapped that in the javascript just to make the acript a bit more re-usable.