I can give you the Spanish perspective specifically, as immediately after the signing of the treaty of Paris of 1783, the Spanish ambassador to France (the Count of Aranda) sent a report to the King of Spain. He foresaw the USA becoming an "irressistible colossus", among other things due to the advantages a federative republic offered. I translate his words:

I mistrust that the new power formed in a land where there is none to contain its projects will incommodate us when it shall be in condition to do so. This federative republic is born, so to speak, pygmy, for it has been given shape by two powers, Spain and France, helping with their forces to make it independent. Tomorrow it will be enormous, so far as it consolidates its constitution, and later shall it be an irressistible colossus in those regions. In that state, it will forget the benefits it has received from both powers and shall think only about its own enlargement. The freedom of religion, the ease to settle people on immense lands, and the advantages offered by that new form of government shall call in peasants and craftsmen from all nations, for man goes where he thinks he shall improve his fortune, and within few years shall we see, and deeply lament, the rise of the colossus I mentioned before. Enlarged that Anglo-American power, we shall think that its first goal shall be the entire possession of the Floridas in order to dominate the Mexican Gulf. Taken that step, shall it not only interrupt our commerce whenever it wants, but it shall aspire to conquer that vast empire, which we will not be able to defend from Europe against a large, formidable, power established in that continent and bordering that country.

The count of Aranda was impressively politcally savvy, but I think that he could not have been the only one to see this coming. The whole idea of a confederation or a federal system was absolutely not alien to an Aragonese as Pedro Abarca de Bolea, count of Aranda, for before the decrees of Nueva Planta, and the Berwick decree, the territories of Spain did function like a confederation, and even the territories of the Crown of Aragon had been some sort of confederation under the monarchs of Aragon. This was also known by Juan Romero Alpuente, who comments in 1808 (Peninsular War), and compares the USA to the crown of Aragon. I translate:

I abdicate, then, in favour of my great nation these august rights, for they can only be faithfully exercised with a well established Parliament, with removable proprietors and solemnly appointed by all of you, or drawn by incorruptible chance, in every element like the American United States, or my glorious kingdom of Aragon whose great princes would have always been great without the abuse of the obedient castilian forces and constitution

The only thing new for the Aragonese count, or for Romero Alpuente would have been the republic, but that would be far from the truth. Republics had been known since the Roman times, and even more recent times had known highly succesful republics known for their wealth: Venice, Genova, Florence, or the Dutch Republic. Having removable officials, subject to accountability and responsibility was an advatage in and of itself. Alpuente does not mention it explicitly but a Parliament with inmovable, id est permanent, members would be an oligarchy, which would lead to corruption.

In Aragon there was some sort of shared sovereignty between the king and the parliaments, notably evidenced by the protocol of the Cortes, where the Cortes (formed by members of the "three arms", ecclesiastical, royal, and military) would make their petitions to the king in first instance, with the king being second. This lead to the king having to cave to the demands made by the Cortes if he wanted any sort of levying of taxes done by the Parliament. That somewhat primitive checks and balances is not inappropriately equated to the United States, where power was exercised by both the President and the Congress.

Sources:

Aranda, conde de (1783), Memoria secreta presentada al Rey de España por el Conde de Aranda, sobre la independencia de las colonias inglesas en América, despues de haber firmado el Tratado de París de 1783, manuscript in the BNE, reference MSS/12966/33. Transcription from

Zárate, Julio (1884), México a través de los siglos, volume III, Barcelona: Espasa y Compañía. Apéndice, document n. 2, pp. 757-8.

Romero Alpuente, Juan (1808), El grito de la razón al pueblo español. Zaragoza: Mariano Miedes.

Martínez Ruiz, Enrique (1992), La España moderna. Madrid: Istmo

Capmay y Montpalau, Antonio de (1821), Práctica y estilo de celebrar Cortes en el reino de Aragón, principado de Cataluña, y reino de Valencia. Madrid: J. Collado