Illegal aliens serve specific purposes for those in power:

1. A cheap exploitable workforce
2. A scapegoat to distract the underclass from pursuing the things that would actually be in their interest to pursue

Conservatives complain that illegal immigrants are "taking American jobs," but this is in part the result of their anti-immigrant stance. See if you can follow this:

1. Mexicans (for example) come to the U.S. seeking work. (Supply of Mexican workers goes up.)
2. Certain employers are willing to hire Mexicans disproportionately because, being illegal, they have no protection from the law and thus can be paid less and treated worse. (Demand for Mexican workers goes up.)
3. The availability of work to illegal immigrants encourages more Mexicans to risk it and come to the U.S. (Supply of Mexican workers goes up.)

Those that seek to demonize illegal immigrants are helping to keep them in the shadows, and thus are helping to fuel this process, which leads to more illegal aliens, which helps those in power consolidate their power and keep the rest of us down--by means of the two reasons given above.

Thus fighting illegal immigration encourages illegal immigration, and those in power who seek to stir up resentment of illegal aliens in the masses are likely doing so because they have a vested interest in keeping them around. How's that for hypocrisy? They say that they want to get rid of illegal immigrants because they want as many of them as possible.

The real answer for how to get rid of all illegal immigrants is to render them legal.

Make it so that all illegal immigrants are legal and thus:

1. Cannot be deported.
2. Pay taxes.
3. Have every incentive to report employers that are paying them less than minimum wage or exploiting them in some other way.

This would reduce the demand for the labor of immigrants that are currently classified as illegal (since the workforce is no longer more exploitable than the citizen equivalents) and thus also reduce the supply of immigrant labor (since less opportunities for work would discourage more people from coming over).

And all those that do come over would be visible, paying for their spots through taxes, and protected from unfair working conditions.

(Many immigrants that are currently classified as illegal already are paying taxes:
http://reason.org/news/show/122411.html)

While we're at it, we should force all companies that want to be involved with the U.S. to adopt working standards that are at or approaching those of U.S. workers for any workers they employ anywhere.

If you are a U.S. based company, you shouldn't be allowed to simply start exploiting workers once you leave U.S. borders. The U.S. standards for how you treat workers should apply wherever you go. And if you exploit workers somewhere else, you should face the same legal sanctions as if you were doing so here.

And if you are not a U.S. based company (and especially if you are from the U.S. but want to set up shop somewhere else to avoid the rules) you should be forced to adopt U.S. standards for your workers or have your access to the U.S. market cut off through an "unethical corporations" specific embargo.

All of this should help to keep jobs here in the U.S. and/or improve the conditions for workers abroad.