The general sentiment, I gather, was pretty much that partisan attitudes were unpatriotic and just unwise.
This sentiment was rooted in the classical education a lot of them had. In classical political theory, parties and factions are by their nature interest groups pursuing selfishness and personal gain, corrupt influences on the polity. Virtuous statesmen who legislate and rule in the public good don't need factions, because the public good is obvious and easily understood according to that theory. This was the way pretty much everyone thought about politics: Virtue meant there could be no parties. To the extent you had parties, you lacked virtue in your government.
Observe that many constitutions written a bit longer ago do not include a reference to party systems. It used to be the norm that political groupings were loosely formed, more like shifting coalitions, ofter in different contellations depending on the subject. Politician X and Y might work together opposed to politician Z when one topic was concerned, and all three might be united on another topic, and on a third topic X and Z might work together against Y.
This was often the case in England before 1776 - there were loosely fixed factions, but these were 'blurry at the edges', so to speak - and I think the Founding Fathers just expected it to turn out much like that in the USA. In fact, they probably imagined a system like that, and wanted to generally urge all of Congress to be less divided into fixed factions. The desire was to have a Congress filled with viruous patriots who would put the res publica over personal opinions, abstain from forming factions, and honestly debate every subject without partisan interest. Some Founding Fathers certainly believed that having a republic would more or less automatically lead to a more virtuous national character.
So in reality, they did little to nothing to actually stop parties from forming. They never even imagined that before long, America would have entrenched political factions that were far more sharply divided and far more fixed than those in Britain.
So this is pretty much wrong.
The entire government designed in the Constitution was meant to prevent the factions and parties. They had had several years of experience with independent government under the Articles, they knew what the state governments looked like. They understood how quickly powerful factions could form. They had a whole 'science of government' they consulted to understand why.
They designed their government to wash out the interests of particular groups by creating large Congressional districts (usually only a few tens of thousands of inhabitants, tiny by our standards but huge next to state representational districts), then set these House members up for longer terms than was usually acceptable (we think our modern politics of permanent campaigns is bad with two year House election cycles -- Massachusetts anti-federalists were vociferously against that term because they had decided their experience with annual legislative elections proved that an annual term was the only adequate security for their liberties!). These large districts and long terms were supposed to allow the virtuous, Enlightened gentlemen they expected to dominate the government to rise above the narrow interests of local factions (too small in these large districts) and win election by default.
Similarly, the Senators were supposed to be as long serving as they were to act as a deliberative branch of the legislature whose less political and more long-viewed chamber culture would act as a break on the expected occasional tumult of the House. Having them appointed by the state governments was supposed to allow those governments to choose their most virtuous citizens to send to the august chambers of the Senate.
And that's also why they wanted the President chosen as a single man instead of as a council. They figured that a single, virtuous mind in charge of the government would be a break against the kind of factions they were used to seeing form in the Confederation Congress whenever they tried to make executive decisions. Of course, their entire design of the Presidency was surprisingly short on institutional limitations because the entire design of the Presidency was based on the assumption that George Washington would be the first President, the living embodiment of republican virtue to the Founding Generation (while we learn a lot more about his refusal to run for a third term is a symbol of this virtue, he was already famous at the time of the Philadelphia Convention for the act of surrendering his sword and his general's commission to the Confederation Congress after the Revolution -- an act that had given him a global reputation of already mythic proportions). They figured he didn't need those kind of limitations.
And then they separated the whole thing into three branches so that what factions and parties did form would be unable to exert control over the whole government at one time.
It didn't work because they didn't do a great job understanding how elections and politics would actually function at that level. There was probably never a time when the Federal government was actually 'working as designed'. Factions formed immediately and the political culture tore itself apart because nobody could cope with them on a political/ideological level. The Washington administration literally couldn't imagine the anti-Administration/proto-Democratic Republican party as a legitimate political force. The administration saw itself as the legal government embattled by corrupt, self-interested extra-governmental forces intent on preventing it from achieving the public good it thought it was pursuing. These men didn't have a theoretical frame of reference to work with and had to make it up as they went along.
Interest groups, factions, and partisan politics would maintain an uncomfortable relationship with American political culture for decades to come, only really bursting out with any kind of justifying political theory with Jacksonian Democracy, which was self-consciously resplendent in self-interest and factions. The entire Spoils System you learn about in school was supposed to be about rotation in office, where everyone got the chance to serve in public office and the possibility of a office-holding aristocracy was cut off. Instead it turned into a massive patronage system that would drive political evolution for the next half century and assassinate a President. This continued right up until Civil Service Reform in the late 19th century.
So the answer is that they did a lot of things to try and prevent parties and factions, then planned somewhat around the failure of their system, and totally failed to plan for what would happen if everything went wrong at once. The whole reason it has survived, however, is because -- although it never worked
as designed -- it has worked well enough to sometimes, every once in a while, work
kind of like it was designed to work. The Revolution of 1800 (leading to the first democratic transition of power between opposing factions in a peaceful manner in the Western hemisphere), the rise of Jackson and the toppling of the Bank, the rock solid will to fight the Civil War and abolish slavery, the above mentioned Civil Service Reform, the New Deal and the resolve to fight and win in WWII, the victories of the Civil Rights Movement, all the kinds of things you learn about over and over again in public schools occurred because, from time to time, the Federal government is capable of rising above narrow interest politics and pursuing what at least looks to a reasonable observer like the public good at the time. It isn't always right but no one is ever always right about complex questions of state.