With the number of people who refuse to buy anything if it's not on Steam I doubt that will happen.
I know, but I can dream. :P
As vocal as that crowd is, there wouldn't be enough of an audience to support a locked down Valve only console.
The cost would be more than next gen consoles as Valve can't afford to subsidize hardware and make it back on game sales like Microsoft, Sony, or Nintendo can. Unless we have another 599 US Dollars! incident, a device made out of PC hardware will cost more unless it's low end.
It wouldn't get a big push from major retailers. Gamestop might be ok selling Steam gift cards, but try getting them to push a no used games system and see how far it gets. Also when people come in to buy a console for their kids for Christmas, they won't go for the unknown one that won't let Jimmy trade games with his friends.
They would have to convince developers to support their version of Linux on the machine. If they used Windows, it would be prone to being cracked open easily, plus they would have to pay Microsoft for every console sold. Getting even the majority of games from Steam working in Linux would take a huge effort of which Valve doesn't have the man power. Companies like EA and Activision get far bigger sales on other consoles than PC to bother porting games to Linux or Valvebox.