Some folks in the US argue that the country should close its borders, not only to illegal immigration, but to legal immigration as well. Regardless of where you fall on those issues though, I would suggest we look abroad to see the results of similar policies. In that light, I would argue that Japan offers a great example as to why closing the borders, without pursuing other conservative policies, does not work.
Let's take a look at Japan. Basically, while they have a conservative no-immigration policy, the rest of the government is fairly liberal: ridiculous amounts of debt relative to GDP, generous social welfare programs, especially for the elderly, and liberal attitudes towards premarital sex and working women.
What have these policies produced? Decades of economic stagnation, fueled by a declining population, resulting in reduced clout on the world stage, especially against competitors such as a rising China. In short, these policies have failed.
Now, let's take apart these policies.
Clearly, the spending needs to stop. Think about it as if you were a person who let their interest payments continually compound on each other. At some point, you're not even going to be able to make your interest payments. Lenders are then going to stop giving you money, since they'll realize that they'll never get it back.
That brings up the question of what to cut. The answer is obvious: the welfare programs that are not producing real and clear-cut economic value in the immediate moment. That means support for the elderly. Yes, as an Asian-American, I know about the Asian reverence for the elderly. However, that assumes that the elderly are wise, and not selfish parasites who would rather not sacrifice themselves for their own children, as has been done for generations. It sucks, but they need to at least pull their own weight, since there aren't enough children to do it for them.
But what if there were enough children to do it for them? Then those children could directly take care of their elders. But there won't be enough children if women are in the workforce, and men can get sex before marriage. If there's one thing you can always count on, it's for people - male and female - to embrace hedonism, once freed from any constraints on it.
In the past, the constraint on both sexes was society. For men, they could only get sex after marriage, so their powerful sexual drive ended up being channeled into becoming a productive father and member of society. For women, they could only get comfortable provisioning after marriage, so that powerful desire ended up being channeled into becoming a loving wife and mother.
Today, however, the following changes have happened:
1) Women are in the workforce, which frees them from the need to seek a provider, which leads to,
2) Premarital sex being accepted, resulting in the top 80% of women having sex with only the top 20% of men, which leads to,
3) The bottom 80% of men giving up and becoming celibate herbivores, contributing little to society, which leads to,
4) A declining birthrate and economy, which leads to,
5) Not enough children and resources to support an aging population.
Thus, the final piece in the puzzle of a declining Japan is to stop women from working, in exchange for men being stopped from having premarital sex. Add cutting spending on useless programs such as welfare for the elderly, and now you'll have a system where individuals have their own incentives to rebuild Japan. And you can still have your no-immigration policy, if you like. But whether that is good or not is another debate.