It's fair to say that a key component to traditional Van Tillian presuppositionalism (of which I still number myself, though in an attenuated way) is the universal knowledge of God thesis (UKT). UKT is taken (mainly) from Romans 1. It can be stated thus:
(UKT) All men have knowledge of God.
But UKT, as it stands, is vague. Almost all sides could agree with UKT as stated, though they would also disagree with each other as to what UKT means. Consulting some standard commentaries bear this out. For example, Barrett, Cranfield, Fitzmyer, and Zeisler are representative of those who claim Paul is only claiming that this knowledge is attainable by men, not that all men have it, or that it is "in" them. Others, like Moo, Schreiner, Witherington, and probably Murray (because I interpret him recognizing his Van Tillianism, though he could fit in the latter category), say this is a knowledge all men have. Others, like Barnett, Morris, and Wright, are vague (thanks to Steve Hays for rounding up all the relevant comments from these commentators for me). Involved here is that there is some textual ambiguity in the Greek. The knowledge could either be taken to be manifest to them or in them. Both sides have a pedigree and it’s not obvious which reading is correct. Add to this that they do not specify what they mean by 'knowledge,' and whether they consider it in its post-Gettier condition or not. Nor do they specify what they mean by "all." Given the fact that many are Reformed, it's not obvious that "all" means all for them! Other views that weigh in are those like the Westminster Confession of Faith. But the statement on natural revelation is vague. It's not clear they meant to argue for an ability or a possession of knowledge. And, if they left it open, it's not clear what is meant by 'knowledge.' The positions are diverse among the Reformers, and the Reformed Scholastics (as Muller's PRRD makes clear, also cf. Sudduth's forthcoming book on natural theology). Not only that, but when interpreting Paul in Romans 1, we should beware of mapping the precisions of modern epistemology onto Paul's language in Romans 1.
As for how some Van Tillians have understood Romans 1, the knowledge of God has been considered in more detail. For example, Greg Bahnsen tries to be more philosophically precise than the theologians. This knowledge is actual knowledge, not just a disposition to know (cf. Bahnsen, VT: R&A, p.222). This actual knowledge is the basis on which men will be held accountable before God (ibid, p.438, 181). It is a "foundational apologetic insight" (ibid, 179). This position is what is used to defeat the reductio that Van Til's position implied that unbelievers don't know anything (ibid, 181, 174 n.74, 208 n.100). Their knowledge of God accounts for the fact that they know a great many things about creation, often times more things than believers. This knowledge is understood as justified true belief (ibid, p.181). Bahnsen and other Van Tillians also view the "all" here as all. That would mean infants and the severely mentally handicapped. So, this knowledge is actual knowledge all men have. So we can add to UKT an Actualist component (as parsed out in the previous sentence), thus:
(UKTA) For any human being S, S has actual knowledge of God
For our purposes, we can bracket out infants and the severely mentally handicapped from UTKA. Though I believe it presents a thorny and strong problem to the UKTA thesis, the present concern isn't to hit actualists with this specific problem. Bracketing out the above groups, I propose a more precise definition is to follow David Reiter's position as expressed in his Faith & Philosophy article on the subject at hand, (Reiter, Calvin's "Sense of Divinity" And Externalist Knowledge of God (F&P, 15, #3, 1998).
I use the UKTA acronym, though it is absent from Reiter's terminology. He used SD, as in, "sensus divinitatis." In discussing Calvin's UKTA Reiter pauses to take notice of an objection to his initial parsing of UKTA:
 For any human being S, S knows that God exists.
The objection is that perhaps Calvin only means "mature or adult humans."
Reiter notes Calvin's claim that the sensus divinitatis "is not a doctrine that must first be learned in school, but one of which each of us masters from his mother's womb and which nature itself permits no one to forget, although many strive with every nerve to that end."
But Reiter finds it appropriate, "nevertheless", to qualify  for the following reasons:
i) Even if Calvin means to assert a knowledge of God at birth or some stage prior, it doesn't follow that he means to assert that human beings possess this knowledge earlier.
ii) Apropos (i), consider a conceptus C. If C is a human, and Reiter believes it is, then  implies that C possess propositional knowledge.
iii) Apropos (ii), we do not know that a human conceptus even has the capacity to have propositional knowledge. It can’t see, why think it knows?
So (i) --> (iii) make it reasonable for Reiter to amend :
[1*] For any sane human being, if S has any propositional knowledge at time t, then S knows at t that God exist.
If we let the term 'cognizer' mean 'human being who has some propositional knowledge,' then [1*] is equivalent to the claim that all cognizers know that God exists. And so this allows that some humans, perhaps due to being at an early stage of development, are not yet cognizers.
Reiter adds one more qualification to UKTA to account for the mentally damaged.
[UKTA*] For any sane human being (cognizer) S, if S has propositional knowledge at t, then S knows at t that God exists.
So, for our purposes, UKTA* is the actualist position we'll attribute to Van Tillians. It allows infants and mentally handicapped to have this knowledge if they are sane cognizers. But if one wants to quibble about that, it also can be read as disqualifying them. It allows us to bracket off the question about whether we can justifiably claim that infants and the like have actual knowledge, cashed out in post-Gettier analysis, that God exists. It is also not the purpose here to look at views of the UKT that understand the term 'knowledge' to mean something other than justified or warranted true belief. These other views are fully compatible with natural theology, and are not sufficient for a robust Van Tillianism. Bahnsen, Frame, Oliphant, and Van Til all take the knowledge unbelievers have to either be justified true belief, or warranted true belief (Oliphint is representative of the latter locution).
Having adequately set up the position I'm bringing out the worry against, I'll now set forth the dilemma:
 The two positions to take on justification or warrant are, broadly, either internalist or externalist.
 If one is an internalist about justification or warrant, then one sets the bar of knowledge too high such that not all men could have knowledge of God because not all men have access to the adequacy of the justifying grounds of the belief under question.
 If one is an externalist about justification or warrant, then the "no conscious believed defeater" constraint means that not all men have knowledge of God because some believe that belief in God is defeated for them, and one cannot know what they believe to be defeated.
 Therefore, either one sets the bar of knowledge too high such that all men do not know that God exists, or the no conscious believed defeater constraint is such that all men do not know that God exists.
 Therefore, not all men know that God exist.
If  is true, then that presents a major problem for Van Tillians who used the muscle behind UKTA* to remove a lot of objections, and move their own position. A couple immediate problems are that the basis for all men’s guilt is now removed, and the rejoinder to the reductio about some unbelievers knowing nothing is back in play. Obviously other problems lurk in the shadows.
1. I think  is fairly obvious, as it is even admitted by internalists. I also do not see them overcoming Bergmann's worries for internalism. Therefore,  is the premise to attack. Namely, the no conscious believed defeater (NCBD) constraint.
2. NCBD has strong intuitive appeal. Michael Sudduth spells out the NCBD condition this way in his IEP entry on epistemic defeaters:
On Bergmann’s view, a person S has a defeater for his belief that p just if he consciously takes his belief that p to be defeated, and a person S takes his belief that p to be defeated just if S takes the belief that p to be epistemically inappropriate. For the latter, S must simply take himself to have good reasons for denying p or good reasons for doubting that the grounds of his belief that p are trustworthy, truth-indicative, or reliable. It isn’t necessary that the person have what are actually good reasons for the negative epistemic evaluation of his beliefs. It is only necessary (and sufficient) that the person take himself to have such reasons, and Bergmann places no restriction on what kinds of considerations might play this role for the subject. So on Bergmann’s view the no mental state defeater condition (as requirement for knowledge) is really a no believed defeater condition (Bergmann, 2006, p. 163). (emphasis original)Indeed, some may say that it is irrational to reject belief in God. And so it is. The evidence is plain and obvious. It would be irrational to deny the nose on your face, and so the same with God. Even more so. Or, so sez me. But the NCBD constraint doesn't fail if it is an irrational belief doing the defeating. As Sudduth says, "My belief that I have hands is unjustified if I believe (however irrationally) that I’m a brain in a vat, even if it’s more reasonable as a policy of belief revision to give up the belief that is less rational or less warranted" (ibid).
One possible rejoinder to the NCBD constraint is to claim that one doesn't really believe his defeater, or he knows it is false, based on self-deception. The former seems problematic as even Bahnsen allowed for real belief (but, some like Audi, take it that one only avows the alleged defeater; he only says he believes it) in the non-existence of God. The latter is more promising. How could a belief that you know is false defeat a belief that you know is true? But, there are multiple models of self-deception. It's not clear which one, if any, is correct (cf. Perspectives on Self-Deception, eds. McLaughlin and Rorty, California, 1988). Also, this view is dependant upon a UKTA* reading of Romans 1, it's not clear that that reading is correct or that this response doesn't beg the question against one's interlocutors. Moreover, the self-deception arguments are highly dependent on external causal stories (e.g., motivations), but the NCBD objection is highly subjective. All that matters is that one believe that p is defeated for him. The self-deception arguments seems to only be relevant if we move away from the more subjective accounts, then. But this seems hard to do (cf. Bergmann, Sudduth).
3. The last argument is that it seems hard to see how NCBD holds in cases like this:
(*) S believes that he doesn't exist because S is convinced by (the late) Unger's arguments, therefore S doesn't know that S exists.
It seems hard to see how (*) could be true. How could we fail to know a thing like that? But (*) seems disanalogous to cases like belief in God. It's not clear that belief in God is epistemically certain like belief in your existence is. What would the argument that it is look like? (Strong modal) TAG? But TAG, as I understand it, is something like the Osama Bin Laden of apologetic arguments. It's been bombarded with rockets and is hiding out in the caves, licking its wounds.
You will note that this is only a dilemma for VanTillians by subimplication. Really, it is a dilemma for any who hold to a UKTA* thesis, whether classical, evidential, cumulative case, or any variety of presuppositionalism. Given the high level of importance traditional Van Tillians have placed on a UKTA* reading of Romans 1, though, if the above argument is cogent (the form is valid and the premises appear to be true) then traditional Van Tillianism seems to have some worries that affect what these Van Tillians have claimed is a key component to the viability of their project. It may need some serious remodeling to keep the ship afloat, then. At least that's the tentative conclusion of this exploratory post. The good news is that I don’t think UKTA* is essential for an “attenuated” Van Tillianism. Many key, and important, insights remain in tact.