Your own summary simply repeats the fallacy. That someone must pick up the tab does not imply that the tab must be larger than it is today, or that the tab must be paid for by this particular chunk of money. It does not follow. It is not a logical argument.
It isn't even about libertarianism. It doesn't even rise to the level of an argument against libertarianism, because it isn't well-formed enough to even be called a proper argument. "We need a thing" and "We need more of a thing" are two completely different arguments, and you shouldn't allow one argument to be substituted for another without noticing.