Throughout our reporting inside the Republican Party over the past few months, one person kept showing up: Mike Lindell, MyPillow chief executive and election denier.

At the Republican National Committee’s winter meeting, he ran to unseat the party chairwoman, Ronna McDaniel. At the Conservative Political Action Committee in Maryland, he couldn’t walk 10 feet without being cornered for a selfie. And more recently, he was a part of news coverage about the Dominion lawsuit and Tucker Carlson’s ouster from Fox News.

While plenty of people don’t take him seriously, Lindell represents, maybe better than anyone else, the challenge facing the Republican Party in this moment: an establishment trying desperately to satisfy its base, despite evidence that their extreme beliefs are costing the party elections.

After months of reporting on that dynamic, we talk to Mr. Lindell and Ms. McDaniel, two people who sit at opposite poles of the party.