One of the biggest problems the Republicans have right now is that it's leadership is seen as disconnected from the base and is certainly not in alignment on many key issues with conservatives in the House of Representatives.
This is attributable to the power that the position of Speaker of the House has amassed over generations. The Speaker selects the committee chairpersons and thus those positions generally reflect his politically ideology.
From time to time it is necessary for a political party to realign with the voters who put them in power to make sure the leadership is in fact leading consistently from the base. Conservatives in England did this most famously in 1923 forming what is to this day called the 1922 committee. The name is more a reflection on the general election of the year and not the party's withdraw from the David Loyd George coalition, but I digress.
The best thing for the GOP to do right now would be to give the power of committee chair positions back to the members. Chairs could be nominated and then voted on prior to the selection of the Speaker. This would remove the primary cause of division between the leadership and the base of the party and result in more effective governing. By eliminating petty infighting and quite frankly brown-nosing to the speaker the party could focus on the issues once the leadership was in place.
This simple change would also keep the Speaker tied closely to the majority of the party. As it is today the Speaker's power is buttressed by people he puts in committee chair positions. A handful of politicians fiercely loyal to the speaker can control the narrative and the legislative agenda. One who crosses the Speaker can pay a heavy price and the party further fractures.
Making this change now will also help to unite the party in time for the November elections. There is some indication that not only will the GOP gain the Senate but may even pick up more than eight or nine seats. Removing this divisive practice and loosening some of the Speaker's control would go a very long way towards this goal. Once seated Congress could then focus on fixing the issues important to the base.