Given the amount of infighting within the GOP over the last few years, it is fair to ask whether it is likely that the party would ever formally split. The answer is no, and the reason is that the predominant Reactionary and PBP factions are natural allies on the issues that matter most to them. In the case of the PBPs, the issue is tax cuts and deregulation; Reactionaries don’t benefit much from pro-business legislation, but they tolerate it because, in their Victorian way, they think that returning “their own money” to the wealthy is OK. In the case of the Reactionaries, the biggest issue is benefit cuts for the “undeserving” poor (in their view, mostly minorities); the PBPs are more than happy to go along with that, as it saves them money.
The issues on which the interests of the two factions are completely inconsistent are free trade and immigration. If the GOP ever splits, you can be reasonably certain that it will be over one or both of those issues.