One way to get a green card is through a job offer in the U.S., as most people who are interested in immigrating know. The offered job must be full-time and permanent—permanent in the sense that the employer expects the need for your services to be ongoing, not temporary or seasonal. Theoretically, any full-time, permanent position can be the basis for a green card, from housekeeper to physicist.
As a practical matter, though, physicists are generally more likely to end up with green cards than housekeepers—as you might expect. For one thing, under the system of numerical limits for green cards, each year more slots open up for people with advanced degrees than for "unskilled" workers, while at the same time fewer people are qualified to compete for those slots. And then there is the requirement to demonstrate that the employer couldn't find a qualified U.S. worker for the job on offer to you: Generally, this will be easier to show for a physicist than for a housekeeper.
But that wouldn't necessarily be true for any given individual physicist or housekeeper, because a lot depends on the way the facts of your particular situation play out under the rules and procedures for employment-based green cards.
Consider, first of all, the process known as "labor certification."
If you are an illustrious physicist, one who enjoys international recognition, then you and your prospective employer can bypass the lengthy process known as "labor certification" altogether. (For a description of these "priority workers," see Employment-Based Green Card Options.)
For most jobs, though—even jobs like physicist that require advanced degrees – the U.S. employer must demonstrate to the satisfaction of the U.S. Department of Labor (DOL) that no qualified U.S. worker is willing and able to take the job. To do this, the employer undertakes an actual recruitment process, advertising the job according to strict DOL specifications and offering at least the going rate of pay. (For a detailed discussion of the recruitment process, see Employer Recruitment Requirements Under PERM.)
If the recruitment turns up even one qualified U.S. worker willing to take the job, then, although the employer is not required to hire the U.S. worker, the job nevertheless cannot be certified for a foreign worker. That will bring the green card process to an abrupt dead-end.
Since physicist qualifications are rarer than housekeeper qualifications, labor certification generally favors physicists over housekeepers. But labor certification is always testing a particular skill set against a particular pool of available workers. Suppose that a particular housekeeper possesses some uncommon experience or knowledge that is indispensable to the would-be employer – the ability to speak Dutch, for instance, when the employer is an elderly man who lives alone and only speaks Dutch. So long as fluency in Dutch can be defended as necessary for the job and the local labor pool is not teeming with Dutch-speaking housekeepers, a labor certification for a Dutch-speaking housekeeper can succeed.
Aside from the question of whether a labor certification can succeed, though, you have to consider whether an employer will be willing to go through the process for you.
Labor certification intentionally burdens employers in order to make sure U.S. workers don't lose out to foreign workers. The Labor Department requires that all the costs of labor certification be borne by employers, not employees – and this includes any attorney fees as well as the advertising costs.
What is more, employers must also bear the time costs. Even if the employer hires an attorney to help with the labor certification—a very good idea given the complexity of the process—the attorney cannot simply assume the burden and run the show. The Labor Department explicitly prohibits the employer's attorney from direct involvement in the recruitment, insisting the employer review resumes, interview apparently qualified candidates, and report why particular candidates do not meet the requirements of the job.
Statistically, again, the burden imposed by labor certification probably favors professionals and people with advanced degrees over other workers, as there are probably more employers needing this type of worker badly enough to take up the burden. But the analysis for any given labor certification is always based on the individual applicant, so if you are a Filipino specialty cook with an awesome repertoire of sauces and marinades, you may well find the requisite highly motivated employer.
Even the most motivated of employers, however, may be daunted by the long waiting time for a green card under most categories of employment.
Under the system of numerical limitations governing the yearly distribution of green cards, the demand far exceeds the supply in the categories covering most jobs, causing backlogs to develop. The wait for a green card can take years for many kinds of jobs, and it's worse for workers from some countries than from others. That's trouble if you want to start working or living in the U.S. right away. (Doing so illegally will only hurt your ability to get the green card.)
Nonimmigrant (temporary) work visas, on the other hand, can be obtained relatively quickly. Being able to work initially for your sponsoring employer in nonimmigrant status might well prove crucial: It is hard to imagine many scenarios in which an employer would offer you a job, go through the green card process with all the attendant cost and effort, and then wait months or even years for you to start work. (See Nonimmigrant Work Visa as a Stepping Stone to an Employment-Based Green Card for a more detailed discussion.)
However, only a very few nonimmigrant categories authorize employment, and each category authorizes a fairly narrow and specific type of employment. Even though the kind of employment that supports a green card is defined broadly as any permanent, full-time job, you might have to find your way through one of these narrower nonimmigrant categories, just because of the waiting time under the yearly numerical limits.
Depending on supply and demand, the wait time for unskilled workers is sometimes actually no longer than for professional and skilled workers. Skilled and professional workers nevertheless enjoy an advantage as a group, in that more nonimmigrant categories apply to them, making it easier to work for a U.S. employer during the waiting time for a green card.
Once again, though, the analysis must be particular for any given employer and employee.
Any offer of a permanent full-time job could serve to found a green card under the right set of circumstances. Perhaps your sister has just invested in a dry cleaning business in New Jersey and you are an accomplished seamstress. Can your sister help you get a green card by offering you a job doing custom tailoring through her shop? You would do well to consult an immigration lawyer for help with the analysis.