A truly dysfunctional GOP majority would be one that unpredictably passes Democratic agenda items, in a way that antagonized or demoralized GOP voters. Or it would pass legislation so unpopular as to ruin the chances of a Republican candidate for president. The GOP-controlled Congress’ theoretical unpopularity (reflected in every poll) is in fact the unpopularity of the institution and of government generally. The people that vote keep sending them there. And as long as a viable Republican candidate emerges from the presidential primary, he or she will have an almost even shot at winning the White House and giving the House majority things to pass.
The only fissure within the Republican Party that is truly dangerous in the long term is the one over immigration, which has divided Republican donors and voters. But this is the manifestation of a larger populist/elitist political divide that cuts across American politics altogether. And still, this is nothing like the substantial regional divisions that hounded the Democratic House majority in the mid-20th century.
The House GOP majority will begin to be functional again once it is matched with a Republican president who can deliver their constituents the goods that come with occasional compromises. And it will also be functional again under a Democratic administration if it shrinks in size, and operates under the discipline caused by a precarious electoral situation.