One may think that.... but it is simply not the present reality.
(And I am saying this with all seriousness, not being flip about it.)
There will be no pulling together, the party is way too fractured for that to happen.
The base is *totally* alienated from the party apparatchiks.
Take a moment and think back over the past several years..... what event can you cite that would give you reason to see any reconciliation taking place? From what I see, the chasm is just growing wider and deeper with each passing year. I could be wrong, but I don't think so at this point.
And a goodly contingent of folks marching under the tea partier flag have done nothing more than throw gas on the fire. One of the big problems these people seem to have is an unrealistic belief in the purity of politics. There is a real reason for the saying "those with weak stomachs should not watch sausage or legislation being made." Being an effective representative in a democracy means knowing how to make sausages and make sure that the product ends up with more of your ingredients than those of your opponent, but knowing full well that it will be well-seasoned with your opponent's ingredients. You cannot be pure as the driven snow and uncompromising on every jot and tittle of your principles, no matter how small. You must roll logs if you want to get anything done.
That being said, learning the art of the strategic compromise is hard, and few can master it. Reagan mastered it and that is why he was so successful, notwithstanding that, when he was elected, the GOP espoused some policies that today would be considered left of center - don't forget that Nixon imposed price controls without batting an eyelash.
The GOP leadership understands that intuitively, although few if any of them have mastered the art.
The folks I'm speaking of reject that concept out of hand. To them there is no such thing as a good compromise, no matter how strategic and useful. That is where idiocies like litmus tests come from - the unrealistic belief that what leads to political success is rigid ideological purity, not the ability to know when, where, and how to compromise on one thing in order to get something else that's more valuable.
And that seems to be the basic problem: we have the unreasonable and unrealistic making holy war on the pragmatic, who in turn are not that good at the art of the strategic compromise, even though they have an intuitive sense of what it is.