But how much of the success of liberal ideals is due to the USA itself? IOTL, the US provided a great propaganda and psychological boost to liberal revolutionaries, who could point to it as an example of a successful liberal country. In a TL where the US is much more reactionary, this wouldn't be the case. The other big revolution, the French, ended up killing tens of thousands of its own citizens, committing the first modern genocide, falling to a military dictator, and initiating a quarter-century of continent-wide warfare. If this were the only example of trying to run a country on liberal lines, I wouldn't be surprised if liberalism were much less popular compared to OTL.
We'd have to estimate the importance of class polarization. Plenty of people OTL were undeterred by the deploring narrative of the trajectory of the French Revolution emanating from the victorious reactionary upper classes; these controlled the bastions of high culture to be sure and we might underestimate how much revolutionary spirit there was for that reason; it was the upper class narrative that tended to be enshrined in widely available histories, novels and other analyses. The more revolutionary classes were not daunted and did produce literature of their own, not to mention word of mouth agitation and verbal family lore. But the literature tended to disappear from libraries and so forth, or never be granted a place there at all.
Of course revolutionaries had their own cautionary take-aways from the record of such trajectories as that of the French First Republic or the outcomes of 1848, largely concerned with avoidance of
reactionary dictatorships; the Bolsheviks being on the lookout for "another Napoleon" or "another Napoleon III" is part of the story of how Stalin slipped under their radar (acknowledging also that the difference between Stalin and most other probable contenders for control of the USSR, or more famous if also more improbable ones like Trotsky, was a difference of degree and style, the Party having long adopted "democratic centralism" with more and more emphasis on the latter part of the phrase.
In short it is not so clear to me that the USA was the major shining light for European revolutionaries OTL. I do think most people veering more or less left of center had some kind thoughts for the American example, but the farther left they went the more critical reservations they had as well; for Marxists any pro-American sentiment would take the form of hopes that the American masses might move drastically and rapidly--away from being apparently rather appallingly bourgeois that is!
Your point is worth considering carefully but in a rather more nuanced way I think. For one thing while "given" the OTL French Revolution I think any American reaction would just shift the focus of European radicals more back to their side of the Atlantic, and no great weight rested on the American example after the Napoleonic wars, still the contemporary American example was probably more critically catalytic in France itself in the 1780s! Would there be a First Republic at all without the American example?
Well, the Constitution was drafted and adopted just a handful of years before the great French risings of 1789.
A Marxist analysis is often caricatured, especially by people who don't understand Marx very well, as cartoonishly simple, a simple two-class civil war between a monolithic proletariat and equally monolithic bourgeois ruling class. Now one reason I respect Marx so much is that I think, after the transition to liberalism and the firm establishment of bourgeois capitalism has been accomplished, indeed society does trend strongly to actually be roughly described by that sociological model, but even then serious and careful Marxist analyses are more nuanced than that; the roles of various subdivisions and classes that at least conceive themselves as "middle" classes are very crucial. Still more were Marx's analyses of actual situations on the ground, notably in his famous "Brumaire" autopsy of the trajectory of the '48 in France and the rise to power of Louis Bonaparte, focused on important subdivisions of the broad categories of classes.
Basically, in the 19th Century, the "project" was the establishment of liberalism, of the bourgeois capitalist order, first of all. Naturally the more radicalized lower class firebrands looked beyond this to socialism in various forms, but center of gravity of power remained the rising bourgeoise, and many people a Marxist might suggest, speaking frankly with them, should throw their lot in with people lower on the social ladder in fact saw good prospects for themselves aiding movements led by and for interests higher up--indeed as a general rule in any social unrest, other things being equal the smart way to play it safer is to ally with some champion among the more powerful.
For America then to turn more rightward, and more to the point for the American people to appear to accept it as a done and settled deal, would throw some cold water on some of these sectors then. But it would actually embolden others, people one might judge more rightward than the dismayed ones, but relative to the situation on the ground in Europe, clearly still among the progressive bloc. They'd feel safer playing with red revolutionary fire.
So to a first approximation, I'd expect the USA going meekly (at least apparently) and whole hog Hamiltonian would have essentially a null effect. Mainly because the time span for the cold water, damping some lower middle class people and invigorating upper middle class people (and their allies in the upper classes) to have either effect in France is short, and insofar as the US example (as opposed to other factors, like the tight financial spot backing the American Revolution put the French monarchy in, which are unchanged anyway) was catalytic, the major documented effect was among the upper classes, notably the nobility--rather than fearing the OTL trajectory of events in America as an existential threat to their privileges, it made movements among the salon classes bolder in seeking revisions away from monarchial absolutism toward a more constitutional order with themselves having a more active say in government. It was with an eye toward offsetting the pretensions of the nobility that Louis XIV called the Estates General, ostensibly about a tax raising process. If instead of the 1787 Constitution, we adopted a more Hamiltonian one, that would I think only encourage the nobles to assert the timeliness of France moving forward on similar lines, and lull the King's wariness about the revolutionary potentials of the Third Estate and cause him to put all the more hope that these commoners would prefer to help him check the nobles. Now, would the less apparently democratic new American order dismay and daunt the leaders of the Third Estate and the more impetuously populist nobles like Lafayette? I really don't think it would; relative to the existing French order even Hamilton's program would look like progress, and the French were not shy about boldly going beyond American examples and doing it their own way. Some would be quieter and less resolved but others would be louder and bolder, and the complex process once rolling would bring forth new waves of hope and enthusiasm regardless of what is happening in America.
So I don't think anything done in Philadelphia in 1787, even something as reactionary as making a rougher and more aristocratic figure than Washington King, and putting down risings against this quite violently, would by that late date derail 1789 in France. Mind, earlier PODs involving the ARW being lost by the Patriots or the whole thing being defused by negotiations and settlements somehow might be much more game changing in France.
Not that I think either American alternative would be very likely, and the former--a rebellion that flares up, costs the Crown dearly but the Crown victory costing the colonists still more dearly, and a repressive restoration of Royal/Parliamentary power in America--more likely than "simply" negotiating away the crisis, for I think the crisis had deep roots in American society diverging in ways little noted but not entirely unseen by astute observers on both sides, and these could be hammered into acceptable sullen compliance with a Crown and Parliament that would learn some necessary lessons in the fray, but not simply talked away peacefully. Very frank talk might have led in theory to a settlement mutually agreeable, but the British side would have to make concessions they would not like to and not see the need to until too late, so I discount this option as realistic. In retrospect the American rebels were in a good position to win out ultimately and had motives to break loose of the British system that they did not clearly understand and recognize before the crisis but which came more clearly to mind during it.
And one of these deep rifting factors I think is that the Americans were becoming both democratic and bourgeois--in other words, deeply liberal.
In practice, no Hamiltonian or for that matter my opposite proposal of ongoing ramshackle Articles regime would stand without seeming, to American eyes, to be satisfactorily compatible with the developing and emerging American social order. I have acerbically pointed out that as American society did and political practice did develop, it actually conformed pretty well with Hamilton's broad notions. So perhaps had he been a bit more astute about mythos and terminology, refraining for instance from ever referring to his strong President For Life as any kind of "monarch." Analytically in the terms of the day, that term would apply of course, but the rhetorically smart thing would be to let his critics claim that and to have some pettifogging distinctions handy that would defuse the charge and put the critics in the wrong--for eventually at any rate, Americans could and did accept the "monarchial" Presidency.
Perhaps in truth his system would have no hope of adoption no matter how carefully sold, in his generation, before the evolution of the confluences of interests among the powerful he foresaw but perhaps discerned their strength prematurely. The Patriot generation was quite present and its spectrum went farther left than the clique in Philadelphia, as they knew well. It might be that a century had to pass before the American people would drift into accepting Hamiltonian forms and thus his notions were basically too advanced (as a shrewdly realistic system, I am not suggesting it was actually "progressive" in the usually left-polarized sense of the term common today, though in terms of doubling down on bourgeois rule it could justly be called just that).
What might have thrown more cold water with a more generally damping effect on the spectrum running from radicals frankly hoping to turn the world upside down to reformers hoping to fix the system would be the American system disintegrating into a bunch of squabbling mini-republics with many of them falling fast into various kinds of autocracy, and the American continent embroiled in frequent war and being played off against each other for imperialist gain, even if no crowned monarch ever formally seized any of them. I suspect even that would only slow things up a bit in Europe.
The USA existing at all, under almost any terms avoiding disintegration, would have served its purpose of revolutionary inspiration already once the British negotiated the truce.