Let me point out that you just mentioned the current shutdown as evidence for a high level of intelligence. I ... really ... didn't think you would do that.
It's a perfect example. It's happening because there are opposing logical viewpoints that are extremely strong due to the educated conditioning of those viewpoints. If there weren't such highly educated people involved in this clash, the will to bend on either side would have been more prevalent.
The main thing here is that both sides have very different personal motives. The GOP understand that if they continue to allow a stream of southern immigrants to come through asking for asylum, it will be hard to turn them down and as a result they will end up weakening their hold on power since most southern immigrants will vote for Democrats due to the Dems consistently doing all they can to appeal to lower class and supporting the expansion of racial diversity in seats of power, while the GOP generally stand more for the status quo in that regard and appeal more to the white majority base.
Therefore, LOGIC dictates that the GOP strongly want to create as much difficulty for immigration as they can and they find a great many arguments to appeal to their voters to earn their support for any policy that will achieve this, namely in this case budgeting for a southern border wall. Many of their people, educated as they are, understand that this is the real issue at hand and support that wall.
For the very same reasons, the Dems stoutly refuse to allow it to happen, not JUST because it runs counter to their own growth of political power, but because they feel a deep disagreement in regards to fundamental value differences. Rather than fearing a loss of racial superiority, they believe that America is not weakened by racial diversity and divided by language barriers, but are strengthened by welcoming in all points of view into our process. They believe more open borders is a moral position, particularly when we have a prosperous nation, that those who wish to come here do so to find those opportunities they lack where they come from, and that all should have the right to seek that and be included in it.
Just as logically, the GOP see these immigrants as 'invaders' who wish to take (share in) our prosperity, thus spreading that wealth thinner still. Both are logical conclusions - both coming at this from opposite values.
I think we ALL know that it doesn't matter if the wall works to create an ROI or not, it's a matter of creating a message to those who would come here: "We only want you if you add measurable value and wealth to the company(country), and are thus likely to be a Republican capitalist. If you don't... if you simply seek to share in American wealth, do not come. If you cannot buy the ticket, you cannot take the ride."
If it wasn't so obvious that this is a serious division in values this issue represents, obvious because those on both sides are well educated, then the negotiability of this matter would be much easier and the value of getting the government back up and functioning to eliminate the pain of the conflict would be 'felt' as less important to endure. Anarchy would have been put to rest much faster than it will be.