1. The only reason there are jobs that "americans won't do" is because they pay too little. Thus, increasing the supply of labor through illegals serves to keep wages depressed, in essence creating a continuous underclass of non citizen which I personally view as immoral, since it is a small step above slave labor.
2. If you work in America, in a just system, every worker should be entitled to the same protections that other workers get. A level playing field for employment is essential in a (somewhat) free market.
That all being said, here is the plan:
1. Set up a working employee identification system, perhaps run by the social security administration. Require all employers to check work eligibility status. If employers are found who are not doing this, fine the employer heavily. Multiple occurrences should include jail time for the management responsible.
2. Set up an efficient guest worker program with Latin America and Canada. Potential workers should show up, apply for work eligibility, and after a background/education check should be put into the eligible labor pool. The application process should be designed to take no more than a few weeks.
3. The department of labor should provide statistics by geographic area on wages for unskilled labor. Any business seeking to hire these potential workers should have to pay a rate of 25% higher than the average unskilled labor wage. All businesses are required to provide high deductible health insurance and injury/disability insurance for the temporary workers they hire. (This is intended to encourage wages to move up to a level where citizens will actually consider them).
4. Employers will specify the time frame for the temporary worker, the temporary work visa will be good for the worker and their family for that time period. If they are terminated, they may remain in the country for a period of 6 months, if they don't find work in that time, they have to go home. If a temporary worker has gainful employment for more than a 3 year period, they may apply for fast-tracked citizenship for their immediate family. Out of work but present temporary workers go to the front of the hiring queue to prevent unnecessary shuffle.
5. If at any time a temporary worker commits a crime that is more than a misdemeanor, their status is to be immediately terminated and they must leave the country.