I imagine that the American usage of "conservative" and "liberal" in the political context has some connection to the British usage of those terms in the historical context. The Tory and Whig parties in Britain began using the terms "Conservative" and "Liberal" around the time of the parliamentary reform and Corn Law debates -- roughly the 1830s and 1840s. The Whigs, which were closely identified with the urban mercantile interests, espoused free trade, whereas the Tories, which drew their strength from the "country" interests (i.e. the landed gentry), favored protectionism. When the Peelite
wing split from the Tory party and went over to the Whigs in the aftermath of the repeal of the Corn Laws, they brought the "liberal" label with them (they had been called the "liberal conservatives" to distinguish them from the "ultras"). In a sense, then, Robert Peel was the founder of both modern political conservatism (with his publication of the Tamworth Manifesto
) and modern political liberalism (when his followers infused the Whig party with their ideals of free trade "classical" liberalism).
I'm not sure when the terms "liberal" and "conservative" first came into use in US politics, but I imagine that the usage paralleled that found in Great Britain. "Liberals," on the whole, were urban, mercantile, interested in electoral reform, and dedicated to free trade. "Conservatives," on the whole, were rural, agricultural, resistant to reform, and dedicated to protectionism. In the post-bellum nineteenth century, however, it would have been difficult to label either major party "conservative" or "liberal." In that era, for instance, the Republicans were more likely to be the free traders and the Democrats were more likely to be the protectionists. By the first half of the twentieth century, however, Republicans became more associated with protectionism while Democrats became more associated with free trade (and it looks like those positions have reversed once again in the wake of NAFTA).
The notion of "big government liberalism" versus "small government conservatism" played little role in this period, since there was really nothing but "small government" in the US before the 1910s. Social welfare legislation, after all, was largely unknown before that time -- and Republicans were just as likely to offer those kinds of laws as were Democrats.
I would surmise that, as the terms "conservative" and "liberal" became more firmly attached to the parties' economic platforms, they also came to be attached to other positions espoused by the two parties. So if, for instance, there was a "conservative" position on the tariff, one could assume that the same person would also have a "conservative" position on international relations or social welfare or public works. Terms that had primarily economic meanings would, by this process of association, be transferred to non-economic issues.