I hate to say this, but unless ET escapes or intentionally calls some sort of attention to them, I think we're being way too optimistic about TC being caught any time soon.
Nobody knows if they had help. Nobody knows whether TC's computer searches and instagram posts were real or if they were a diversion. Nobody knows if he still has the Rogue, and if he does, what color it currently is and what plates are on it. They may or may not even be in the US. Nobody knows if he's camping, living in a rental/motel, or has some other arrangement.
Further, TC is very average in appearance. He's not especially tall, short, fat or skinny. He has no tattoos or scars (at least not that are readily apparent.) He may or may not have changed his appearance again since Walmart. On the other hand, to me at least, ET looks different in every picture I see of her. I personally would never have given the girl in Walmart a second look - and again, she might look radically different than that now. Throw in the fact that she's experienced with special effects type makeup, and she could probably make both herself and TC up to be unrecognizable.
Add to that the fact that most of the country isn't actively looking for her. For the last month, everyone's been distracted by the giraffe. At this point, if people (including police) are actively searching for anybody, it's most likely the shooter from Cleveland.
We all think that in these days of "big brother" watching everything, it's impossible to lay low and not be found - but look at the number of illegals who do it. They're not all out working on farms or as day laborers or maids, either. There are plenty of skilled people who get paid under the table (if anyone questioned it, TC could tell them he was collecting disability or on workmen's comp, and that's why he wanted to stay off the books.) For that matter, he could probably get away with using someone else's ID, as long as he didn't run up a bunch of bills or otherwise draw attention to himself.
It wouldn't surprise me a bit if TC is just sitting back and laughing at LE, especially if I'm right and he's been giving them false leads and sending them on a wild goose chase.