Just because it's Linux doesn't mean SSH (or another protocol, like Telnet) is installed and activated. These are proprietary devices and the OEM would likely ensure none of those were working because they don't want you changing the system. This kinda makes sense for support reasons.
If it is indeed running Linux, you can ask for the source (they're distributing it when they sell the televisions) and work from there, but that's tedious and beyond my skill level.
You could try their support. You never know, they might just be down with the idea and tell you how to connect.
Before I sent this, I did do some preliminary searching to see if there's a solution out there already. I was unable to find anything - though some folks seem to think you can possibly connect but you'll need to brute force the credentials. You can look into that, but I don't think too many folks (our regulars) are regularly hacking their TV.