Thanks for the update.  The work around didn't function for me originally because I was also loading the recaptch js inside the jquery dialog box.  Which created a race condition between loading the js source and executing it.  I fixed it with jquery getScript:

<div id="captchadiv"></div>
        <script type="text/javascript">
            $.getScript("http://www.google.com/recaptcha/api/js/recaptcha_ajax.js", function () {
                Recaptcha.create("6Lf8oc8SAAAAACgdybPC2Mx2eX0CUFDCBSwXCYQw", 'captchadiv', {
                    tabindex: 1,
                    theme: "red",
                    callback: Recaptcha.focus_response_field
                });
            });

In case that helps anyone else.

Thanks for your reply Victoryismine.