What invalidates his position is the complete illogic and fecklessness of his argument. Bundy exemplifies the contradiction of American Libertarianism, which is that our staunchest libertarians have always been the western ranchers, ala Bundy, who are, themselves, vigorously unrepentant welfare queens (just one example: the grazing fees Bundy refuses to pay are hugely subsidized by the federal government; they're priced far, far below market value). Their issue with the country isn't that people are on the dole. It's that the wrong people are getting a piece of that dole.
They say wisdom's the ability to tolerate paradox. If so, Bundy's a Buddha. There's also his claim of being an American patriot - and waving flags everywhere - while denying the existence of the United States. That's some profound non-linearity, but the best counterargument the Left can muster has been to scream "Racist!".
The Left, which has seen pretty much every worthy movement degraded by the participation of goofballs, flakes, and extremists of their own base, should know better. In fact, they do know better! But it's easier to scream "Racist!" than it is to dismantle a faulty argument (just as it's easier for a conservative to rail against those damned hippie liberals than to grapple with their arguments). If you're a racist (or a damned hippie liberal), everything you say or do is without value or basis. It's a word one can utter to refute not merely an argument but a person's right to make any argument at all (it's all about tolerance!).
Jon Stewart, alone, did a pretty good job with Bundy's argument on its merits (see below). He's an idol for the Left because he's the only one apparently able to parse and express anything in a coherent and persuasive manner. But even he missed the central paradox of the patriotic flag-waving brio of Bundy and his posse as they deny the existence of a United States of America.