You know, looking at the evolution of the Republican Party over the last 24 years, I think one could very well say that it has become more and more parliamentarized, i.e. it behaves a lot like the kinds of political parties you see in parliamentary systems, both in its behavior in government and opposition as well as in its inner workings, despite the formal legal institucional structure of the Constitution and of the way political parties have traditionally worked in the United States.
You could observe some of this behavior already in the 1990s, when Newt Gingrich was for all intents and purposes a parliamentary opposition leader. Later, one could even compare the failed Clinton impeachment to a failed confidence measure, the kind that happen now and then in parliamentary systems. And during the time George W. Bush (Republican) had Republican majorities in either or both houses of Congress, the Republicans and the Republican administration acted like an absolute parliamentary majority government. When Barack H. Obama (Democratic) became president, the Republican Party behaved exactly like a parliamentary opposition party, both in the minority (congressional hearings, poitless or not, legal or judiciary ooposition, common opposition instruments in parliamentary systems) and with divided government with astonishing party discipline ("cohabitation" in the sense used by the French, although this would be more like a forced "cohabitation").
And now, ever since Donald J. Trump actually became President and later in opposition, the GOP has, in addition to the informally parliamentarist practices of the last decades, a party leader who remains as leader (although informally) and functions as such (selecting candidates, enforcing party-line discipline, etc.) even when the Republican Party has been in opposition, again both under conditions of being a minority opposition and under divided government.
The United States doesn't have the legal or formal structures of a parliamentary system and certainly the sort of adversarial dynamic between parties ("the spirit of faction") and also inside the Republican Party has always been rejected (or only tolerated to the extent that it was inevitable) in American political culture. This itself is problematic, apart from the inherent, ubiquitous, and obvious defects of parliamentarism and weimarization, as opposed to a properly balanced and checked presidential system.