On one of the best presentist accounts we have, namely that of Trenton Merricks, statements that some proposition p was or will be true are to be understood as embeddings of p in the context of a was or will modal operator, which modal operators are analogous to modal operators like M (possibly) or L (necessarily) or in a work of fiction or ought to be the case. Moreover, even if p is the sort of proposition to normally have a truthmaker, was(p) and will(p) do not have a truthmaker. Call this "modalist presentism."
Here is a problem for modalist presentism. There are a number of contexts in which we stand in the same kind of relation to a proposition about the past or the future as to an analogous proposition about the present. One kind of case I've already discussed in another post, the case of induction: we treat claims about past, present and future on par with respect to induction. A different set of cases are provided by certain non-first-person attitudes (this idea comes from Parfit). If my child is to undergo a painful medical procedure this afternoon, I will be pained at his undergoing the painful experience. Suppose that I am today out of causal contact with my child. I do not think it should matter much to my attitude right now towards the child's experience whether the experience has just occurred, or is now occurring, or is about to occur. And even if there is a difference, there is a common core of compassion in all three cases. Similarly, if I have heard that a friend will today receive a teaching award, I will be glad for his sake. Supposing I am unable to attend the ceremony, it will not matter vis-à-vis my gladness whether he has received the award five minutes ago, or is receiving it now, or will received it in five minutes.
The non-presentist has a way of explaining and justifying the common core of the inductive and emotional attitudes: in all cases, the attitude is a response to the reality of some situation. The feeling I have towards my child's actual pain, whether past, present or future, is different in kind from the feeling that I have towards facts of the form Q(my child is in pain) where Q is some modal operator like M or in a work of fiction. (The case of L is different, but that is because Lp entails p.) Likewise, I treat past, present and future occurrences on par for inductive purposes, and recognize the difference between these and possible or fictional occurrences. In fact, we might even say that a good test for whether I take a situation to be real is whether the situation enters into my inductive and emotional attitudes in these kinds of ways.
But for the modalist presentist, my child's having suffered pain is related to my child's presently suffering pain in somewhat way that my child's possibly suffering pain is related to my child's actually suffering pain. So now we have a problem for the presentist: to explain why it is that there is a pattern of attitudes that are equally appropriate towards situations within the scope of was and will operators as towards present situations, without adverting to the reality of these situations.
Here's a different way of formulating the worry, one that will affect even non-modalist presentists. It seems that what makes it appropriate to have the same attitude of grief or joy at various true propositions, and to engage in inductive reasoning about such propositions, is that these propositions have a truthmaker homogeneity: they are all made true by similar kinds of things. But the presentist denies truthmaker homogeneity between reports of past, present and future pains, as well as between reports of past, present and future raven blackness. The present-tense reports have ordinary sorts of truthmakers, like black ravens or people suffering. The past and future tense ones either have no truthmakers (Merricks) or have truthmakers of a significantly different sort (Bigelow, Crisp) from the present tense ones.
It might be thought that while the presentist has trouble explaining and justifying the lack of difference in these kinds of attitudes, the eternalist has trouble explaining and justifying the difference in first-person attitudes. I care a lot about whether a painful experience is past, present or future. But this is not a problem for the eternalist. For the justification of an attitude often lies not just in the objective features of the situation towards which one has the attitude, but also in a relation to the situation. That a situation is earlier than, simultaneous with or later than an attitude can affect whether the attitude is appropriate or not. And this indexical difference seems to matter a lot more in the case of situations that involve one oneself.