Immigration, even illegal immigration, is a net benefit for the country. We would probably be better off deporting all Trump supporters than deporting all undocumented immigrants.
Open immigration would by even very conservative estimates double the world's wealth.
We don't need to keep Mexicans out of the USA any more than we need to keep New Yorkers out of Florida.
Building a wall is a huge waste of resources. I might be ok with it if Trump wants to squander his entire fortune paying for it personally (the most modest cost estimates are approximately equal to what he claims as his total net worth, so it would leave him with about to the amount of wealth he deserves), but not if it would require using imminent domain to confiscate private property (as Trump loves doing).
Migration is a natural right. If any government is to be allowed to infringe upon that right it needs to have a very compelling interest in protecting other natural rights. I could support measures to limit the movement of violent criminals or those carrying highly contagious diseases, but current regulations are ridiculous.
We don't really need "deportation," just occasional extradition or quarantine.
Economic protectionism is never a good enough justification. That always means making most of us worse off in order to help those with political connections.
Issuing only a very limited number of visas in limited categories is not acceptable. We should not require any visas at all.
Voluntarily working for an employer and being paid what the private parties agreed upon (to do anything that would be morally permissible if done without remuneration) is also a natural right. There should never be any government intervention, save perhaps to ensure informed consent as to either party's qualifications or lack thereof. If an employer wishes to hire only natives then the state should not stop him, but neither should it stop any employers from hiring illegal immigrants.
Almost all of Abraham Lincoln's arguments against slavery apply just as well to the right of migrants to work to support themselves.
Our contemporary immigration regulations are the modern version of the Fugitive Slave Acts. I only hope that future generations will recognize them as such.
If legal immigration was made easy for everyone wanting to come here for peaceful purpose (and if we also end the "War on Drugs," which is far more harmful than the drugs themselves), there would be very little incentive for anyone to come here illegally. That would make it much easier to address the few remaining cases of those who still would try to enter illegally for malicious purposes.
Protecting the culture is also a rather stupid rationale. Cultures are a fluid set of values and practices which individuals ought to be free to accept or reject. (Most cultural values from across the world cannot stand up to scrutiny and probably ought to be rejected.) All cultures evolve primarily by borrowing from other cultures. Attempts to describe the nature of any particular culture tend to degenerate into rather insulting parodies. No one should be bound to blindly follow traditions of the culture in which one happens to have been born. Viewing foreigners' cultures as hostile is probably the most effective way to prevent those immigrants from interacting with their new neighbors enough that they become assimilated and mostly join the dominant culture instead of maintaining the traditions which the natives fear.
Residency and citizenship are different issues though. Granting anyone citizenship as soon as he crosses the borders seems imprudent. I frankly think it is unwise to grant anyone citizenship automatically based on happenstance of birth. Those who will be voting and influencing public policy should have to sign some citizenship contract demonstrating informed consent, perhaps after passing some tests to ensure at least a basic understanding of the Constitution. I recognize that this would require amending the constitution, but it is a deeply flawed document in need of a major overhaul anyway.
p.s. The Great Wall of China was never intended to stop a Mongol invasion. It was mostly meant to stop successful raiders (Mongols and others) from retreating back home with all their loot. Its guards were so corrupt that they often helped the invaders cross both ways in exchange for a share of the stolen goods. At best, they helped send messages to various army outposts in order to let the Chinese troops know where to go to track the raiders down to punish them and take their booty as bonus pay. The goods rarely found their way back to their rightful owners, unless the owners were rich and powerful.
Building the wall was also a huge waste of resources, funded by centuries of high taxation and forced labor which were much more harmful to the Chinese commoners than the Mongols themselves ever were before becoming the "legitimate" Imperial government. Even then, the Mongol rulers were not as bad as many native Chinese regimes were both before and after them. Great powers rarely fall to external forces unless their own leaders are so bad that the common man begins to recognize the invaders as a lesser evil.
(Note that the wall was really a variety of smaller walls and watchtowers of very different ages and qualities, originally intended to serve only local areas, which were linked together fairy late. In many areas it is merely a crude fence or a rough mount of dirt, without any of the aesthetic qualities of the portions most often photographed.)