There's also this, not focused on parties though:

Testing Theories of American Politics: Elites, Interest Groups, and Average Citizens

Multivariate analysis indicates that economic elites and organized groups representing business interests have substantial independent impacts on U.S. government policy, while average citizens and mass-based interest groups have little or no independent influence.

[...]

In the United States, our findings indicate, the majority does not rule — at least not in the causal sense of actually determining policy outcomes. When a majority of citizens disagrees with economic elites and/or with organized interests, they generally lose. Moreover, because of the strong status quo bias built into the U.S. political system, even when fairly large majorities of Americans favor policy change, they generally do not get it.

https://act.represent.us/sign/problempoll-fba

Note: I just know this is the study you’re referring to. But I have no clue what the background of the organization is or their research credibility or if the site is just some think tank presenting a separate, independent study

Lol. “Remember that study saying America is an oligarchy? 3 rebuttals say it's wrong.” https://www.vox.com/2016/5/9/11502464/gilens-page-oligarchy-study

Wait never mind, just rereading it and you’re asking for political party, not opinion