Because the debate is multifaceted, I'm going to attempt to address each aspect of the debate individually.
EconomicThere appear to be two main economic arguments made against amnesty and for stronger border enforcement:
1) Illegal immigrants are a net drain on the economy. I believe this claim is simply false. A poll of economists conducted by the Wall Street Journal found that:
On balance, nearly all of the economists – 44 of the 46 who answered the question – believe that illegal immigration has been beneficial to the economy. Most believe the benefits to business of being able to fill jobs at wages many American workers won't accept outweigh the costs.
2) Illegal immigrants are bad for lower-class American workers. This appears to be true, but not very significant:
Nearly 80% of economists who responded to questions about immigration in the latest WSJ.com forecasting survey said they believe undocumented workers have an impact on the bottom rung of the wage ladder. Twenty percent believe the impact is significant, while 59% characterize the effect as slight. The remaining 22% said there is no impact.
It also occurs to me that we don't oppose computers or robots despite the fact that they take jobs away from people, because we think the trade-off will be worth it. Workers who lose those jobs will be able to secure different jobs created in large part by the extra wealth provided by the increased productivity. I don't see why immigration would be any different.
One final point. Those who argue that illegal immigrants are bad for the economy don't seem to factor into their calculation the cost of preventing illegal immigration, which would involve construction of the largest fences/walls in the world as well as the deployment of many soldiers along the border. They also don't take into account that native-born Americans are not reproducing at greater than replacement rates, which in the absence of immigrants would make it harder to support retired Americans.
JusticeIt is my impression that this is the underlying motive of normal Americans opposed to amnesty or anything resembling it. Illegal immigrants are here illegally, by definition, so we shouldn't reward them for it. Humans have strong innate negative feelings towards cheaters and, in my opinion, often overreact to them even when it goes against their own self-interest. While I agree that it's generally bad to reward illegal behavior, I think that when a law is so flagrantly and massively violated, it's because the law was impractical to begin with. (Other examples: prohibition and a speed limit of 55 mph.) At some point we have to recognize that even if in an ideal world where everybody followed the law it would be a good law, in reality an unenforceable law simply erodes respect for the rule of law and harms the exceptionally law-abiding.
Some may argue that it's not that the law is unenforceable but that we have chosen not to enforce this. They will point to polls that suggest a majority of Americans would prefer better enforcement against illegal immigration. However, I believe that if and when the public realized what would be involved in seriously enforcing the law (mass deportation, tons of spending, harm to the economy) support would quickly dissipate.
SecuritySome claim that the porous borders are a grave national security threat. I do not believe that this is true, or if it is true, that we can effectively do much about it. All of the 9/11 hijackers entered the country legally. There are between 2 and 10 million Muslims already living in the U.S. We have no shortage of homegrown criminals or gangs. While it is true that Mexican gangs are a problem in some areas and that terrorists might sneak across our borders, locking down the entire border strikes me as a ridiculously inefficient way to deal with the threats. Furthermore, terrorists attempting to enter the country would undoubtedly have vastly more resources than the average poor Mexican immigrant, so enforcement would have to be incredibly severe.
The essential truth of the matter is this: life is not safe. The government can do only so much to protect us. They are happy to, however, make enormous promises about security in order to get votes and money. Take one look at the woefully ineffective war on drugs or the inanity of post-9/11 airline security, though, and it's clear that many of their promises are just wishful thinking. Security would be more effectively increased with intelligence and police work than by erecting the Great Wall of America.