I disagree with your first premise: "based on conservatism." Remember, conservative and reactionary ideologues generally oppose progress, dislike political reform, and are generally indifferent to the concerns of those who are socially and economically disadvantaged. The French Revolution sought to address the concerns of the disadvantaged by dismantling the aristocracy and by attacking the middle-class (épater la bourgeoisie).
Classical liberalism, to which I think you're referring, developed in Europe during the Enlightenment, which inspired the French Revolution. The ideology emphasized civil liberties, property rights, and the rule of law under a representative government. Clearly, these ideas would become very important in the formation of the American republic.
There are certain core ideas that all liberal theorists have in common. Here I include John Locke, Adam Smith (the first thinker to introduce the notion of free markets, or a laissez-faire economy), Jeremy Bentham and John Stuart Mill (Utilitarians), and later, Frederic Bastiat, to name a few. They all appeared to accept Locke's view that human beings were rational and industrious. They all believed that people were generally governed by what gives them pain or pleasure (this is specifically a Utilitarian notion). They all believed in the importance of economic freedom, particularly the pursuit of property and free trade.
Taking all of these ideas together, one could say that liberal thinkers held the individual in high esteem. They believed that people were generally rational, and when brought together, in what Locke called "the commonwealth," they would form a society based on fairness and individual liberty. The role of the state was to be limited. This is especially true for Bastiat whose ideas are very important to the contemporary Libertarian movement.
One could argue (I certainly would) that liberal theorists failed to account for the baser aspects of human nature, particularly greed. The Industrial Revolution led to the exploitation of human labor on several continents. Marxism sought to address this.
Marx wanted a recurrence of the French Revolution of 1789, in the interest of addressing exploitation and ensuring the rights of the working-class. His ideas became popular during the Revolution of 1848, a revolutionary wave that began in France but spread throughout the rest of Europe, ending monarchies and establishing parliamentary governments.
Later in the 19-century, many would come to view Marxist theory as not only a political theory, but also as an aid to human progress. His ideas would often be compared to Charles Darwin's, due to his understanding of human nature and what he deemed necessary for the evolution of the species.
For Marx, the first step in a more humane government was an abolition of the class system. That would mean eliminating the notion of inalienable individual property rights, which the liberals had touted. The unrestricted pursuit of individual wealth had only led to exploitation. It also allowed the bourgeoisie to control the means of production, and to create a culture in which the pursuit of wealth, under any circumstances, had become a noble cause.
As a result of their exploitation, the working-class, or proletariat (literally, "producers of offspring") became disconnected from their own humanity, or what Marx called "species-being." They lived in cramped quarters like cattle; and they took comfort in sex, resulting in more children whom they could not care for and whom they would sometimes kill in infancy.
Marx wanted a government that would dismantle capitalism. He wanted a strong state that would ensure the rights of all classes, but that would particularly protect the interests of the proletariat who were vulnerable to exploitation. The liberals wanted a representative government that would uphold individual liberty and property rights. They believed that people were rational enough to be fair and to respect their neighbors' right to happiness.