There's not an explicit way to ask for more detailed information, no -- basically, ya get what ya get.
That said, Web servers often return documents along with those error codes that sometimes contain useful information, much like the one you got explaining the problem with the SSL cert. For help sniffing out problems like this, check out Fiddler -- it'll show you just about everything there is to know about your server responses.
As for your particular error, it's hard to say; 403 can indicate a few different things. But if you got back a response indicating something having to do with SSL, you may just be dealing with a bad or expired certificate (see this question), or the server may be requiring a secure connection but not getting one. Have you tried just hitting the URL directly with a Web browser, just to see whether you get prompted with a warning indicating a certificate problem, or anything other than an unmediated 403 response?