Now you're talking. Eliminate the reason for illegals to be here, punish any employer that uses them, and they'll deport themselves. When you try and deport people, it gets on the news, Americans get sad, and emotion gets in the way of logic.
Keep the discussion based on laws and economics. Punish the employers. De-incentivize illegals from coming in the first place. Incentivize them to go home on their own. It's not as quick as rounding them up and throwing them on southbound buses, but it has the advantage of being totally feasible and politically palatable.
The easiest way to solve the illegal immigrant problem is to charge higher income, FICA, and medicare taxes for non citizen workers. Once there is money to be made the government will be ruthless in enforcement. Have you ever seen the IRS decide not to go after money due from an employer?
You don't even really need to identify illegal immigrants - there could be discounted tax rates for people with legal visas, but they should still pay more in taxes.
For example, if the FICA rate for a non-citizen was 15% for the employee and 20% for the employer there would be little reason for employers to hire non-citizens unless there truly were no citizens willing to do the work. For non citizen workers there should be a tax on all income, and it should start at say 25%, and it could include a minimum amount every year.
Illegal immigrants pay thousands of dollars each to get smuggled across the border. It would be better for our government to sell non-citizen work permits for the same kind of price, or better yet make the employers pay the work permit fee. How many employers will want to write that check to the IRS?
Likewise, it is entirely reasonable to have different regulations for non-citizens. Making them pay for health insurance, or auto insurance is not an infringement on their rights, since they don't have a natural right to be in the country in the first place. Many countries have specific regulations for visitors - so should we.
Making the IRS the primary enforcer of immigration law is likely to be way more effective than any fence could ever be.
...eliminating the reason for illegal employment....
I wonder if THAT is what Obama is trying to do with our economy....
/sarc