Recent infighting raises the question: How conservative is the GOP?

A few weeks ago, Americans — or, the subset who get excited about these things — were glued to C-SPAN as the House voted 15 times for a speaker.
It was a show of a deep but hard-to-describe division in the party. While the overwhelming majority of Republicans supported eventual Speaker Kevin McCarthy, a faction of 20 Republicans held out. Among their demands were that the House not raise the debt ceiling without deep spending cuts.
What set them apart? To some, the rebel Republicans were showing their ideological purity.