Just a few thoughts on the risk of a war between conservatives and populists on the right:
Conservatism has a long tradition of pluralism, so the attempt to purge all dissenters might at once run afoul of conservative tradition and be politically counterproductive. You can still be a conservative and oppose TPP (and even "free trade" in general--unless Calvin Coolidge doesn't count as a conservative anymore). Likewise, you can still be a conservative and support "amnesty" or "comprehensive immigration reform" or the Gang of Eight bill.
Furthermore, there's room for conservative-populist compromise on a variety of issues. The current populist surge points to the blind spots of contemporary political debates. One of the jobs of political movements is to identify and to speak to underlying problems, so people who want conservatism to live as a political movement have a great incentive to address these challenges. Luckily, conservatives can indeed address them. Conservatives have a lot to contribute to discussions of wage-growth, national self-government, the restoration of competence, civil alienation, and other issues. The tradition of limited government, civil society, intellectual modesty, and personal liberty can very much provide a grounding for a search for solutions to contemporary problems.
Indeed, there are possible harmonies between some conservative and some populist principles (though there are tensions, too). On issues such as empowering local communities and defending the idea of the nation-state, populists and conservatives can certainly much get along. Reigniting wage-growth and strengthening a sense of civil integrity, for instance, could both soothe populist anxieties and advance the aims of limited-government conservatism.
Moreover, if they're interested in gaining political power, populists and conservatives very much have an incentive to work together. Ronald Reagan's majorities were built of both readers of Burke and lunch-bucket workers in Fishtown (and those categories are not mutually exclusive). It might be chic to denounce one's opponents as knuckle-dragging losers and it might be comforting to just scream, Burn it all down! But defending a limited-government republic demands a much more thoughtful and responsive approach to politics.