Conflicts of Compromise

What both parties are also missing is this: Any individual American is also capable of holding views that seemingly conflict, and it is our individual right to do so.

It is the politicians' job to recognize this and work out the conflicts and contradictions through compromise and accommodation. This is what the political culture of a democratic republic requires. It is also what most voters expect, whether they realize it or not.
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I would submit that the politician's job has little to do with compromise and accommodation. The job is advance the interests of their constituents, in a way that said constituents understand is making their lives better, increasing their income, giving them better services or what-have-you. If compromise and accommodation are the most effective path to that, fine. But I suspect that, given similar outcomes in that department, a politician who achieves the outcome without offering the opposition anything in return is going to be seen as more successful than one who gives their voters what they want, but at the price of having to give something else up.

In this respect, one can view retail politics as being a lot like retail - if people have the choice to buy something for $3, or for $5, it's a fairly safe bet which one they'll go for, even if they understand that the extra $2 will go to other people in their community. And even though not everyone will go for the lower price, or the lack of compromise; in the same way that not enough people were willing to pay higher prices to save local small businesses from large nationwide enterprises, not enough people are willing to pay the costs of compromise that candidates can win elections by citing a willingness to accommodate others as a platform plank.

The fact that so much American political discourse has been marked by explicit or implicit stands on self-evident correctness on whatever side a given person may support and/or charges of being willfully perversity on the other side doesn't help matters. Compromise in the face of someone wanting something that seems obviously wrong tends leave people feeling that they've been extorted, and while they may come to expect that sort of behavior from their political opponents, it's unlikely that they're happy when concessions are eventually made.

The perception of poverty, whether justified or not, makes people sensitive to not receiving everything that they feel that they need or that they want. Compromises, which are effectively built on giving something to get something, therefore become less attractive, in favor of outright victory, which (correctly or not) people understand that they are giving nothing to get something. Whether or not a republic requires compromise becomes secondary. And given the fact that Americans have developed a habit of seeing winning elections as an entitlement to having their interests publicly funded at the expense of the losers, compromise is likely the last thing on most people's minds.