I don't think anybody has any good solutions, which means the debate will be especially rancorous, but here are a few things I think:
* Whenever you have a rich nation adjoining a poor one, there will be incredible pressure to migrate to the rich nation, by any means necessary.
* I am not convinced that enforcing our borders (using means that would be condoned by citizens of a democratic nation) would reduce illegal immigration even to a "reasonable" level.
* I don't want illegal immigrants to be abused because they fear going to the police.
* I don't want to deny essential entitlements to the children of illegal immigrants. No child should have to pay for what their parents do. Those who wish to deny children of illegal immigrants health care and education because "they don't pay into the system" -- where do you think that will leave these children in 10-20 years? What options will they have to support themselves? Is such a policy more or less likely to cause them to turn to crime (or to create a permanent 'underclass'), than simply absorbing the cost of educating them?
* The US does an excellent job of assimilating immigrants. Our diverse population is generally at peace, especially in comparison to other parts of the world.
* Guest worker programs carry a great risk of making the guest workers "inferior" to the citizens. Look at Europe -- guest workers there are marginalised and balkanised, and ready to riot at the drop of a pin.
* Any legal means of immigration designed to stem the tide of illegal immigration needs to try to remove the incentive to cheat.
I look at all these basic ideas, and I don't see an easy solution.