Read The Armchair Economist by Landsburg.
What you’ve listed above are results that were built from a long series of proofs and mathematical models.
At the basis of neoclassical economics is the assumption of what it means to be rational. If you imagine a binary relationship, that is some relation between two things, e.g. taller than or older than or hotter than, then these relations can have certain properties. For example, taller than is transitive in that if x is taller than y and y is taller than z then x is taller than z. Another property is completeness, so that perhaps everything can be compared in terms of height.
Neoclassical economics begins by assuming that preferences, i.e. x is at least as good as y (which means that x may be exactly as good as y or x may be preferred over y), are rational which they define as being transitive and complete. Taking this definition, economists use a series of mathematical if-and-only-if statements to come to an if-and-only-if relationship between rational preferences and a certain pattern of choice between bundles of goods, prices, and budgets. Experimental economics is a maturing field that has, as I understand it, shown the rationality assumption to be a pretty good approximation—that it is at least good enough to be useful for predictive purposes.
From there more assumptions have to be added; but they are generally reasonable. For example, it is assumed that consumers do not have lexicographic preferences. This is obviously reasonable because we don’t see people giving up everything they have for one tiny bit more of some specific good. People will even exchange air quality for location, convenience, etc.
The theory of the firm happens similarly. When the two are put together, we can come to our equilibrium results and try to utilize those to make useful predictions. These models are becoming increasingly verified experimentally. There is a growing field of classroom experiments for teaching that utilizes specialized participation exercises to show that the models being taught hold just as a physics teacher uses experiments to show his models are valid. Many “facts” would be considered to be essentially true by many economists.
Macro models work a little bit differently in that actors are assumed to maximize utility and the utility function is given some form that is often ad hoc based on the model used. In some cases the individual isn’t even included at all. The economist then tries to translate the intuitive assumptions into math so that they can be dealt with. There are macro experiments for classroom exercises as well. Whether there are “facts” is sort-of an off-topic question. One can look at the models and agree whether the premises are properly constructed or whether the logic follows properly.
Your examples might be held to be generally true to many economists. As a noncomittal statement (for lack of a better word), yes, cutting taxes would stimulate the economy. But that doesn’t mean that it would be a good thing or that other factors need to be taken into account in certain situations. So two economists may be discussing tax cuts and one may pull out a quasi-Keynesian model to say that tax cuts will stimulate the economy. The other will say this is true given that the model includes assumption Q; however reasons a & b make assumption Q questionable. So a president’s chief economist may say that tax cuts will stimulate the economy and the charman of the Fed, a guy who wrote a fulsome introduction of praise to an Ayn Rand book of essays, may respond that this is normally true but because the nation is already has such a high debt burden that it would be better to carry a surplus and reduce the debt to improve the government’s financial position if has to go back to deficit financing. This is purely hypothetical, of course.
What you see is not what economists consider or deal with. Your examples are reminiscent of a president stomping down a quaint village street with bolts in his neck and angry villagers behind him shouting, “Fire bad! Taxes bad! Arrgh!” This caricture is not that far from the level of sophistication used in public debates on tax policy. By way of comparison, political discussion of economics is about as sophisticated as the stickers on high-school biology books insisting that evolution is just a theory. If you understand that the public discourse on economics is about as well informed as the public discourse on evolution, then you understand that there is a lot of stuff economists do and agree on that is not on the public radar.
Landsburg’s book is outstanding and everybody who wants a lay-introduction to economics should read that book.
Please note that the above was not intended as partisan hackery, if that is a word. It was intended to give an idea of how far from what economics actually is from what we see in the press. I am confident that the president’s chief economic advisor would make very good arguments for such-and-such tax policy. The disagreements lie in the workings and assumptions of the models they are using, and on the difficult job of teasing out reality from the picture of it shown in the sample data.
I’m confident that I didn’t answer your question, but I do hope I’ve helped you understand that you may not have been asking the right question. That is not an insult or a dig; asking is something most people don’t even bother to do.