Start with his glib conclusion: "Recent events are simply public choice theory in simply public choice theory in action." If we assume there are no irrational actors in politics (an assumption some will consider heroic), then public choice theory explains both everything and nothing. That is to say, if all political interactions are explained by public choice theory, then the explanation itself becomes trite.
On a more substantive note, Cowen pretends that the GOP is a single actor with a single motivation. The evidence suggests otherwise. Political parties are never as monolithic as they might appear, and in current circumstances, the US Republican Party appears on the verge of civil war. If news reports are to be believed, a majority of Republican senators and legislators do not want the federal budget held hostage to Obamacare; and the real problem resides in a relatively small minority of the Party in the House, who are making their own calculations not based on national opinion polls, but based on re-election prospects in congressional districts that have been gerrymandered in a way that rewards extremism. In other words, they do not have to worry about political challenges from the other party, but only challenges from more extreme elements in their own party primaries.
As I have noted before, gerrymandering is the joint responsibility of both parties (operating according to Public Choice theory), and has led to the perverse situation where instead of voters electing public officials, the public officials get to pick their voters.
Thus, assuming Cowen's general assessment of the political calculus is correct, the question becomes, for which Republican senators and representatives is it correct. None of the facts of the current situation in Congress warrant the broad presumption that the entire Republican caucus in both House and Senate believes the conflict will be good for the party as a whole (although it could be that).