Columnist Frank Rich, in the 11/22 New York Times, quotes Matthew Continetti (Weekly Standard-bearer for Sarah Palin and author of The Persecution of Sarah Palin: How the Elite Media Tried to Bring Down a Rising Star), as having "suggested that she recast the populist outrage of William Jennings Bryan by adopting the message, 'you shall not crucify mankind upon the cross of Goldman Sachs' ".
Interestingly, while Bryan ("The Great Commoner") was undeniably a populist, he was a Democrat; thrice the party's nominee for President, as the Gilded Age morphed into the Twentieth Century. Liberals can certainly embrace Bryan as an avatar of progressivism (e.g., women's suffrage, the income tax, anti-trust legislation, etc.), and claim the mantle of populism for themselves, but they may have reservations about Bryan's fervid religious fundamentalism, his views on evolution, and his ambivalence about condemning the white supremacy of the KKK.
Paradoxically, we get into very tall socio-political weeds when we try to align conservative vs. liberal ideals with their seemingly conflicting claims to true populism. A constitutional republic such as ours is, by definition, popular (i.e., "of the people"). Such republics are also, by definition, liberal democracies. Furthermore, the Populist Party of the late 19th Century took a leading role in the Democratic Party and gradually merged with The Progressive Movement; thus, liberals would seem to have the determinative edge.
Historically, however, American populism is largely rooted in agrarian and artisanal working-class discontent with a privileged elite (what Bryan called "the money men of the east"), along with nativism and fundamentalism, all markers for a sort of prairie conservatism going back to the early 19th Century, and even, tangentially, to Jefferson and the anti-Federalists.
One has to conclude therefore that neither side has a monopoly on populism which, like libertarianism, occupies a comfortable tent in both camps.
To note that it is often difficult—even dicey—to try to pigeonhole everyone according to their beliefs is to merely state the obvious, especially since political ideologies—among politicians in particular—are not only fungible, but can be highly susceptible to the way the wind is blowing.
We are, and always have been, a nation of strange bedfellows, but, dang it (as Sarah would say), they're our strange bedfellows and we'll work it out.