Argument from universal consent. The present argument may be said to be independent of any special system of thought. It has been employed by those whose philosophical positions are widely different. It rests simply on the principle that man's intellect is fundamentally trustworthy: that, though frequently misled in this or that particular case through accidental causes, yet the instrument itself is sound: that, of its own nature, it leads, not to error, but to truth. It follows from this, that if the human race, taken as a whole, agrees in regarding a given conclusion as certain, it is impossible to suppose that that conclusion is false. Could a general conviction of this kind be mistaken, it would argue that something is amiss with the faculty itself: that it is idle for man to search for truth, since the very organ of truth is fallacious. Pure scepticism would be the sole logical attitude. In point of fact, man cannot use his intellect without recognizing its trustworthiness. It is its own sufficient guarantee. When we judge, we do not judge blindly: we see that our judgment is true. This being premised, we urge that there is a veritable consensus among men that God exists. All races, civilized and uncivilized alike, are at one in holding that the facts of nature and the voice of conscience compel us to affirm this as certain truth. We do not, of course, mean that none are found to deny it. There is no proposition which some will not be found to question. The pragmatist denies the necessity even of the principle of contradiction. But we contend that those who admit the existence of God form so overwhelming a majority, that agnostics and atheists do not affect the moral unanimity of the race. If, then, the judgment of all mankind cannot be mistaken, we have here yet another valid proof of the existence of God.
Note two key points: the nature of human reason shows up explicitly as essential to the argument, and the claim for universality is that of "the moral unanimity of the race", not the bare agreement of everyone without exception. Walter O'Briant claims in a 1985 article that this is a divergence from the historical tradition, but provides no actual evidence of this: the people he considers as having discussed it are Plato (the Laws passage), Mill, Hume, Herbert of Cherbury, and John Calvin. Of these, Calvin certainly would have known that some people claim that God does not exist; O'Briant criticizes Mill for not getting the argument right, either (and Mill's interpretation would also have avoided the universality problem, since Mill took it as an argument to the authority of mankind generally, especially of its wisest members, which does not require that everyone without exception agree); Hume explicitly qualifies 'universal' with 'almost'; and Herbert of Cherbury is not discussed in sufficient detail to establish that he does commit to strict universality. Thus O'Briant doesn't really seem to have a case that Joyce is wrong here.
O'Briant also argues that Joyce, despite not holding to strict universality, needs it:
Joyce is hung on a dilemma of his own creation. If he uses the notion of consensus as involving merely proportionate agreement, then the belief in the existence of God becomes something about which the human intellect may in particular cases be misled. If he uses the notion of consensus as a universal agreement in P2 [There is a veritable consensus among men that God exists] , then he must deny that there can be atheists or agnostics. [Walter H. O'Briant, International Journal for Philosophy of Religion Vol. 18, No. 1/2 (1985), pp. 73-79]
But there is no real dilemma here; Joyce's argument is that those who are theists of some kind form such an overwhelming majority that 'human intellect may in particular cases be misled' cannot be an adequate explanation of the fact, although it can be an adequate explanation of the small number of atheists. (It's another question whether agnostics should be brought in at all here, since, despite the tendency to lump atheists and agnostics together, the intellectual stances are rather different.) O'Briant seems to think that "the human race, taken as a whole" requires "every human being" rather than "the human race on the whole" -- but it is clear that Joyce is explicitly arguing that the latter tells us something about the nature of human reason, and this is at least not an implausible claim. If it's true, though, then, Joyce can take the first horn of the dilemma without any problem: the argument is entirely consistent with atheists being the particular cases of error, while the general and normal operation of reason shows that these are, in fact, errors arising through accidental causes rather than through reason itself. There are questions one could certainly raise about this argument, but the universality problem is not a serious issue here. (O'Briant does hold, it should be said, that while the argument fails as a proof, it is a reason to take the existence of God as prima facie plausible -- and if he had stuck with just criticizing Joyce on the strength of the conclusion he thinks Joyce can get, instead of arguing that he is hung on a dilemma involving universality, he would have been on much stronger ground.)
It's worthwhile to compare in this regard another kind of consensus gentium argument that does not deal with the existence of God -- the consensus gentium argument that some things really are morally right or morally wrong. This argument does not require that there be no skeptics about morality or psychopaths; it just requires us to hold that the human race, generally speaking, is rational, and that human reason is basically trustworthy, so that a solid consensus is guaranteed at least to be the most reasonable interpretation of available evidence; and therefore that if there are people who diverge from a very solid consensus on this point, it is at least very likely that it is not due to superior reasoning but due to some cause of error.