You can have Python running on the DD-WRT box of course, which will probably drastically slow down your router. You can also generate a public key for the router and append it to a remote host's .ssh/authorized_keys file, but for reason number 1 above, it's probably not a good idea. Now if you have a PC box running Vyatta or pfSense, then you might be able to pull this off with minimum impact.
Can I have a ww-drt install act as a client with Sshuttle and install a public key to require no login?