In surveying, in the Enquiry Concerning Human Understanding, several different possible candidates for the original impression from which our idea of power or causal connection is derived, Hume considers the suggestion that it could be do to our sense of effort (7.15n):
It may be pretended, that the resistance which we meet with in bodies, obliging us frequently to exert our force, and call up all our power, this gives us the idea of force and power. It is this nisus, or strong endeavour, of which we are conscious, that is the original impression from which this idea is copied.
He rejects this proposal for two reasons, only the first of which I want to consider here. This first reason is that we apply the idea of power to things we don't think have experiences of effort or endeavor, namely, God, minds in control of their own thoughts, and inanimate objects:
But, first, we attribute power to a vast number of objects, where we never can suppose this resistance or exertion of force to take place; to the Supreme Being, who never meets with any resistance; to the mind in its command over its ideas and limbs, in common thinking and motion, where the effect follows immediately upon the will, without any exertion or summoning up of force; to inanimate matter, which is not capable of this sentiment.
How much of a problem is this, though? Take a famous case: Hume visiting a friend once sat in a chair (I think the friend was Ambassador Keith), which then collapsed under his weight. (He remarked, I think to the friend's daughters, who were the other people in the room, that their father should keep stronger chairs for heavy philosophers.) Unless we are panpsychists, we can take as given that the chair did not have an experience of trying to hold Hume up, that it did not feel any straining of its parts as it collapsed. Given that Hume doesn't think that there's any contradiction in having an experience without a mind (he takes minds just to be bundles of ideas and impressions and thus not more fundamental than they are), it's unclear that he himself can actually assume this to be true, but let's take it as granted. There is still more to be said here.
One of the most important inferential patterns is analogy. Analogy plays a significant role in Hume's account; he thinks, for instance, that most of our understanding of mental operations depends on analogy. And Hume is, as I've noted before, a maximalist about analogical inference: he thinks analogy has at least some force as long as at least some resemblance exists. As he puts it in the Treatise (SBN 142):
Without some degree of resemblance, as well as union, it is impossible there can be any reasoning: but as this resemblance admits of many different degrees, the reasoning becomes proportionably more or less firm and certain. An experiment loses of its force, when transferred to instances, which are not exactly resembling; though it is evident it may still retain as much as may be the foundation of probability, as long as there is any resemblance remaining.
This account is reaffirmed in the Enquiry (9.1):
Where the causes are entirely similar, the analogy is perfect, and the inference, drawn from it, is regarded as certain and conclusive: nor does any man ever entertain a doubt, where he sees a piece of iron, that it will have weight and cohesion of parts; as in all other instances, which have ever fallen under his observation. But where the objects have not so exact a similarity, the analogy is less perfect, and the inference is less conclusive; though still it has some force, in proportion to the degree of similarity and resemblance.
Now, an important point here is that analogy already has to be involved when we are talking about nisus or endeavor, because we attribute to animals, and indeed to animals very different from us. We only experience our own. But due to the resemblance of animals to us, we have no problem taking them to have something like our experience of endeavor, even though we may well admit that we don't know exactly how they experience it. And if we turn our eyes to inanimate objects, can we say that there is no resemblance to exactly the kinds of situations in which we attribute effort to animals?
Consider our language, for instance. If I say that the chair tried to hold Hume up but failed, or say that the chair strained or struggled to hold him up, you all know exactly what that means. If you see an automobile struggling to get up a hill, and remark, "It's trying so hard!", I know exactly what you mean. And Hume himself recognizes that when we talk about power and causation colloquially, endeavor is often involved:
As to the frequent use of the words, Force, Power, Energy, &c., which every where occur in common conversation, as well as in philosophy; that is no proof, that we are acquainted, in any instance, with the connecting principle between cause and effect, or can account ultimately for the production of one thing to another. These words, as commonly used, have very loose meanings annexed to them; and their ideas are very uncertain and confused. No animal can put external bodies in motion without the sentiment of a nisus or endeavour; and every animal has a sentiment or feeling from the stroke or blow of an external object, that is in motion. These sensations, which are merely animal, and from which we can a priori draw no inference, we are apt to transfer to inanimate objects, and to suppose, that they have some such feelings, whenever they transfer or receive motion.
In this comment we have again the two reasons for rejecting it mentioned ("which are merely animal, and from which we can a priori draw no inference"), but it is, first, not really clear that people are actually supposing that inanimate objects have feelings when they say that an object is straining under the weight of a heavier object, and, second, since we are already having to analogize to attribute endeavor to animals, it's not really clear that we can't just keep analogizing and say that, to the extent that the behavior of inanimate objects is like that of animate objects, we can attribute to them something like what we experience as effort or endeavor. We don't even have to say that we know exactly what it is; the question at hand is not "What is it like to be a chair?" but "Is being a chair straining under Hume's weight in some way like being a human being straining under a heavy load?" If it is, the likeness gives some force to the attribution. If we get the idea of power from the experience of endeavor, then we can attribute something at least like it to the chair.
We can get out of this if we can break the likeness, and say that a chair's straining is, despite the similar language, actually nothing like our straining, so there is no resemblance. But this is not easy -- as Hume notes, the effects (transfer or reception of motion) are similar, so by analogy, one can conclude there is similar endeavor. You could get out of it by the Berkeleyan notion that nothing is like a perception except a perception, but then, if inanimate bodies are just bundles of perceptions (which that notion inevitably requires), it's not clear why it's impossible to say that one of those perception is an idea or impression of endeavor.
So we have the similarity. Analogy falls off as the resemblance falls off, but for a lot of physical actions, there isn't much difference, for that obvious reason that our body itself is engaged in physical actions. If I stoop under a heavy load, in physical terms, it's not actually all that different from a chair sagging under a heavy load. Why would it be? If we can separate off the feeling of effort in the former case, we can block the analogy despite the resemblance. This is what Descartes would do: the feeling of endeavor is a modification of thinking thing, the sagging is a modification of extended thing, and in our case they are causally connected, but they do not themselves have anything to do with each other, so we cannot attribute anything like the endeavor to the purely physical chair. (Descartes would regard that as a mistake like an Aristotelian might make.) But Hume is not a Cartesian; he can't separate off the endeavor as having to do with a different kind of substance.
Hume also says that the idea we get from the impression of endeavor can't be attributed to God or to minds doing things with their own ideas. It's not very plausible to say that we never experience endeavor of will or thought; again, we use language suggesting otherwise all the time. The same argument would seem to imply in the mind case. It would be, to say the least, a remarkable irony if a Humean were to reject endeavor as the original source of our idea of power on the grounds that it does not give us an adequate account of divine omnipotence, but in any case, Hume's own view of the idea of God is Lockean, which is to say, he takes it to be based on our ideas of our own mental operations, so on Humean principles the case of God would stand or fall with the case of the mind's internal operations.
There are reasons indeed not to tie the idea of causal power too closely to the experience of effort, but in the context of Hume's own positions, the claim that one can't be derived from the other because only animals experience effort seems inadequate to the conclusion that he wants to draw. Indeed, it seems to fail entirely. On Hume's account we get the idea of shape from impressions of shape, but nobody thinks that physical objects have the experience of shape, which is something we only attribute to animals, despite the fact that everyone, even Hume, attributes shapes to inanimate objects; and any skepticism about whether a physical object really has shape is irrelevant to the question of whether we get the idea of the shape attributed to physical objects from our experience of shape.
Thus there seems no reason not to recognize the straining of Hume's chair, even allowing that this straining is only analogous to the straining we experience under a heavy weight.