Using jQuery crossdomain (JSONP) to log in - GET might be an issue

I'm building a bookmarking utility that will add a button to another website, and send data back when the button is clicked. If a user is logged in to my service, they get an "ok", otherwise a prompt to log in or register.

So far the initial communication is ok using a jQuery AJAX request and JSONP as the datatype. I'm able to send through the initial data to the server, and have it reply with a form.

Edit: Rewrite to clarify the question:

If I'm sending a login using JSONP (which uses GET), would using https be pointless as the username and password would be in the url?

HTTPS crypts everything, including HTTPS header (this include the URL). So, using HTTPS would actually be a good thing.