A Red Tory is an adherent of a centre-right or paternalistic-conservative political philosophy derived from the Tory tradition, predominantly in Canada, but also in the United Kingdom. This philosophy tends to favour communitarian social policies, while maintaining a degree of fiscal discipline and a respect of social and political order. It is contrasted with "Blue Tory" or "High Tory". Some Red Tories view themselves as small-c conservatives.
Not being an expert on Canadian and British politics, nor being particularly proficient in the comparative study of democracies, I would propose (1) during the Progressive and New Deal eras, such a thing of approximate similarity to "Red Toryism" did exist in the United States; (2) that this tradition was sidelined in favor of a more "liberal" version of conservatism--priding on-paper liberties (at least in the economic realm and certain social spheres) over stability. The first of these proposals is actually more interesting than the second--the latter is easily explainable given America's strong tradition of small-l liberalism. Yet, the "progressive" conservative tradition appears to have its own very strong historical roots in the nation-building efforts of Alexander Hamilton, Henry Clay, and Abraham Lincoln.
My guess is that, within the Republican fold, there were two traditions: one favoring a strong state and a national infrastructure, and the other favoring liberty for business. These two were once symbiotic; there was a shared belief among some in the party that the infrastructure of banks, railroads, etc. could be used to ease commerce while allowing men of talent to rise. Abraham Lincoln is a good example of this; he spent much of his career as a man of merit in a rural backwater, lobbying for economic modernization to reach him. Nevertheless, these traditions departed at some point following the mass industrialization of the United States.
I would think that, on the one hand, you have those who persisted in their belief that those with talent and ingenuity would inevitably rise given the removal of constraints on their activity. On the other you have those that recoiled at the excesses of late nineteenth/early twentieth century industrialization and sought for a way to balance it through redistribution, regulation, and social control. There were what we would now call "social conservatives" in both groups (there were those who believed that the "strong and sober" were more fit than the lazy and drunk; alternatively, we can see the argument that rationalization and destitution erode religion and right conduct). This is how we get the intra-party warfare between progressives and conservatives between, say, 1900 and the 1930s. The Great Depression and the New Deal recast these divisions along new lines, and we see the results in the 1940s and 1950s, with conservatives recoiling at the new powers and reach of the federal government while liberals simply claimed they would better manage it. Herbert Hoover exemplifies both of these traditions in one man: he was a progressive in his party up until the presidency, believing in far-reaching reform, but was still fundamentally a capitalist, and reacted to the Crash with substantial restraint, in part because he believed fervently that one's labor ought to be the determiner of one's station in life--he may have liked infrastructure, but he did not like handouts. By 1940, of course, he was a conservative as the ground had shifted underneath him.
The battle within the Republican Party after 1945 was fundamentally about whether the New Deal ought to be adjusted, trimmed down, and expanded where need be; or if it should be done away with entirely. While (elected) conservatives by-and-large came to make peace with a substantial amount of the new government infrastructure, the decline of support for state planning and intervention in the 1970s owing to macroeconomic and ideological shifts across the entire world brought about the twilight of old style "big government" ("progressive") conservatism. The rising up of the masses was no longer a concern, and a variety of new flavors were in town. In part because of this, and in part because of the rise of the Religious Right, the left-wing of the Republican Party came increasingly to be cast, rather, as essentially small-l liberal on both economics and social policies, rather than as some sort of patriarchal Tory manager or overseer. I think in the case of the US we have a country that didn't have a very institutionalized place for out-and-out moderate state-centric conservatism in the first place (owing to the government's historical reduced role) so it did not survive this transition the same way that progressive conservatism or "Red Toryism" survived in other Eurosphere countries where social stability was always a higher priority.
Another issue that I haven't addressed here is that, owing to the US' geographic distribution, including the locating of the federal capitol far and away from the centers of economic and cultural life, the idea of mobs overthrowing the government rarely been a big concern outside of maybe the Bonus Army incident in the early 30s. So conservatism has not had to address social stability as much as in European countries.
EDIT: Additionally, owing to the US' lack of a formal hereditary aristocracy, the legitimacy of the ruling classes has rested much less on tradition and more on the rhetorical use of such terms as "merit" and "liberty". For similar reasons, there is less of a tradition of downwards redistribution of wealth as part of some obligation on behalf of the aristocracy--American conservatism is less paternalistic in this regard.
EDIT2: The importation of southern Democrats into the Republican coalition during the mid-late twentieth century also probably had a profound effect on the GOP. Suspicion of federal action had new bases, and Thomas Jefferson was suddenly a conservative icon.
