I would use ssh for this instead of netcat.
Just to get some confusion out of the way, I will be referring to the node with VPN access as the "server", and the node without VPN access as the "client".
On the server side you should only need to install and have an ssh server running (in my test I have OpenSSH_5.9p1, OpenSSL 0.9.8r 8 Feb 2011).
On the client side you will need to do the following:
1) in your /etc/hosts file add in the address that your target URL resolves as on the server. I wasn't able to get curl to run DNS lookups through the proxy, which is why this is necessary.
2) setup ssh keys between the server and the client. while this is not necessary, it makes life easier.
3) run the following ssh command to have ssh act as a SOCKS proxy:
user@host$ ssh -vND 9999 <server>
-v is there so you can see what is going on with ssh, -N tells ssh to not execute a remote command - this is useful for just simple port forwarding -D this option is what actually forwards your local requests to the server
4) now you should be able to run the curl command you have above, but add in
---socks5 localhost:9999
Your full command will look like this:
curl --user $USER:$PASSWORD --socks5 localhost:9999 http://$JENKINS/api/json
If I can figure out how to forward the DNS requests from curl through ssh I'll update the ticket.
edit: formatting, awful grammar.