What was the American consciousness like around the War of 1812? Was the country more patriotic, or were they more interested in the ideals of Romanticism? What general ideals would have appealed more to the American public at that time?

First, we should note that the country was deeply divided over the War of 1812. The war was generally favored by southern and western states, while the New England states were bitterly opposed to it. Merchants in the Northeast had little to gain from the interruption of trade with Britain, and they even went so far as to hold a convention at Hartford, Connecticut in 1814 in which they protested the war as an extension of more than five years of policy (including an extended embargo on trade) that had been mostly ruinous for them. Most of them were Federalists, and their opposition to the war would prove ruinous to the Federalists as a national political party. The war of 1812, like the Mexican War almost forty years later, was the source of major controversy in the United States.
That said, the war was also the catalyst for a spirit of nationalism not previously seen in the newborn nation. While arguably different than the Romantic nationalism espoused by many European liberals (and, for that matter, the spirit of "manifest destiny" that would emerge a couple of decades later in the United States), Americans were angered by the burning of Washington, DC, in particular, and they celebrated the result of the war as a validation of their experiment in a republican form of government. The years immediately following the war are sometimes called the "Era of Good Feelings" due to the absence of party factionalism and the celebration of nationalist sentiment. The question seems to assume that "patriotic" nationalism and "Romantic" nationalism were mutually exclusive—they were not—but certainly the nation was awash with patriotism in the years following the conflict. One contemporary European observer said that the war had given the United States a "national character," something that the nation had previously lacked.
https://connecticuthistory.org/the-hartford-convention-today-in-history/