The only way to punish illegal immigration is deportation. I realize its unpopular, but it's the only way. We need to deport people in order to force them to go through the legal immigration system.
In order to reward people for going through the legal immigration system we need to reform it to be cheap, simple, and quick. It should also scale well so that it can handle a much larger number of immigrants.
The best way to do this is to run it like a lottery. Everyone that wants to come to the US gets an account number. Each quarter we deposit into your account a certain number of lottery tickets. The more tickets you have, the higher your chance to win. If you win, you get accepted into the US. We can set it up so that the longer you have been waiting the more lottery tickets you receive. We can also give more tickets to various groups that we want to favor, such as people with college educations and so on. The system is highly customizable just by changing how many tickets a person gets.
We hold a drawing once a quarter, and the winners get visas.
In addition to this I would make it a requirement that you prove you can speak English, hold down a job, and have a legal place to live before citizenship is granted.
I'm sure there are many that believe my stand on immigration is unnecessarily harsh. I am willing to have some compromise, as long as we can stop the flow of illegals and thus stop the deaths.
One method of granting amnesty to illegal immigrants that have been here a long time that might still allow us to discourage illegal immigration by deporting any new illegal immigrants is to have some tests to determine if you have been here a long time. The three tests that I think might work are these:
1) Can they speak English? If they have been in the US for years, they should be able to speak English at least a little.
2) Do they have a job? Anyone that's been here a while has to have some way to survive, so they will have one.
3) Do they have a legal street address? And can it be confirmed?
If an Illegal immigrant can pass all three tests above, and is willing to let the police take a high quality photo, and a copy of their fingerprints for a criminal background check, then I'm willing to compromise with the amnesty crowd and grant them a 2 to 4 year work permit. They will then have 2 to 4 years to apply for permanent residence and go through the normal immigration procedures that every other immigrant has to go through.