We had some interesting times with this one in our company. First step is to double check your settings in Administration>Public Addresses in the VCD Public Console Proxy Address field. Does that DNS name resolve to the IP you assigned to the VMRC NIC in the setup? Try browsing to https://<Console Proxy Address>/sdk/vimServiceVersions.xml and see if it loads.
One other place to check is the VMRC logs, you can find them at:
%userprofile%\local\temp\vmrc-plugin\
%userprofile%\local\temp\vnware-username\
But beware that's where the vSphere client puts its VMRC logs too, don't get them mixed up if you use both on the same machine!
Our issue was due to our network isolation. The clients accessing our VCD instance had no outside/internet access. The VMRC plugin requires the ability to pull down root certs/crl's from the web in order to complete the SSL negotiation on occasion. Last I checked it still wasn't documented but VMware support is now aware of the issue.