Are we a democracy or a republic?

 Actually, we're both.  There was a good article on NPR:

Is America a democracy or a republic? Yes, it is : NPR

"What do we call the system of government in the U.S.? Are we a democracy or a republic?The conundrum is, well, as the common expression goes, "as old as the republic itself."

"But it's not just a question for scholars and semanticists any more."

"Since the election of 2020, supporters of former President Donald Trump have become notably more willing to assert their belief that voting in America is suspect. That Trump won an election he lost. That "millions of ballots" were uncounted or miscounted. That voting by mail was fraught with abuse."

"Despite the lack of evidence, and the judgments of election officials from both parties and judges appointed by presidents from both parties, election denialism has become not only a thing, but a movement. And when critics call this an attack on democracy, some election deniers respond by saying the U.S. is not a democracy, it is a republic."

"Robert Draper of The New York Times published a piece on Republicans who say this in August. He cited a GOP candidate for the Arizona state legislature, Selina Bliss, saying: "We are not a democracy. Nowhere in the Constitution does it use the word 'democracy.' I think of the Democratic Republic of the Congo. That's not us."

"Throughout our history we have functioned as both. Put another way, we have utilized characteristics of both. The people decide, but they do so through elected representatives working in pre-established, rule-bound and intentionally balky institutions such as Congress and the courts."

"The government seated in Washington, D.C., represents a democratic republic, which governs a federated union of states, each of which in turn has its own democratic-republican government for its jurisdiction."

"The relationship between the democratic and republican elements of this equation has been a dynamic and essential part of our history. But it has not always been easy, and in our time the friction between them has become yet another flashpoint in our partisan wars."

"We regularly hear people on the left speak of conservatives destroying democracy, and just as regularly we hear conservatives say Democrats have no respect for the Constitution. To add to the confusion, the two camps often swap their lines of attack and defense. Republicans call Democrats enemies of democracy, Democrats rail against what they see as Republican disrespect for the Constitution."

"And that also makes sense, in a way, as both sides want to be the champions of both democracy and the Constitution, and to advertise themselves as such to the voters."

"Yes, as a polity, we think we are and can be both. We aspire to be both. But in practice that can prove difficult. And in our time, when so much of the public discourse happens on Twitter and cable TV news, the terms have become increasingly weaponized."

"Equality and democracy are under assault," said President Biden on the steps of Independence Hall last week. "We do ourselves no favor to pretend otherwise."

"Biden at Independence Hall used the word democracy 31 times, including three times in one sentence. He used the word republic just twice."

"Republicans, by contrast, have seemed of late to be stressing the role of the republic and its restraint on democracy. Sen. Mike Lee of Utah, an outspoken Republican but hardly an outlier, got considerable attention for saying bluntly on Twitter in October 2020: "We are not a democracy."

"Lee then posted online an explanation of what he meant. It said, in part: "Our system is best described as a constitutional republic [where] power is not found in mere majorities, but in carefully balanced power."

"Lee went on to catalog how difficult it was for majorities in Congress to pass legislation, get it signed by a president and watch it undergo judicial review. Lee's point was that he was OK with all that. It was the intent of the founders."

"In the absence of consensus," Lee wrote, "there isn't supposed to be federal law."

My take:  The Republicans are prevaricating on the definitions of "democracy" and "republic" to push their own agenda, which is that they are not committed to majority rule unless it is in their favor.