The GOP should start working with the President. That would solve the division right away. But of course, that isn't want you meant; right?
What does the GOP need to compromise on now? Higher taxes? More Spending? Making illegals legal? Putting abortion rights in the US Constitution? What?
*Taxes for the wealthiest Americans
*Coming to a consensus on immigration reform that has some aspects of what amounts to amnesty in them.
*Recognition of the need for some social safety net so we don't have to have this idiotic battle about cutting all of it every 2 years.
*A consensus on same sex marriage and the need to extend the right to all Americans.
*Spending cuts to the military.