What does it mean that the woman George W. Bush has picked to be his secretary of labor once hosted a woman who was living in the United States illegally?

It means that a lot of critics are going to be jumping all over Bush and Linda Chavez, but the question we need to be asking is what, exactly, does this mean with regard to her ability to enforce the administration’s policies? This isn’t a new issue; in 1993, Zoe Baird, nominated by Bill Clinton to be attorney general — the nation’s chief enforcement officer — lost her cabinet post because she had hired an undocumented child-care worker and failed to pay the proper payroll taxes.

Chavez’s case is less clearcut, because although she apparently did allow the woman to perform some household chores (as guests often do) and gave her some spending money, it doesn’t appear that Chavez sought her out as an employee. Jesse Jackson’s claim that the arrangement was nothing better than indentured servitude is a little hysterical. Such an arrangement provides considerable opportunity for abuse, but there seems to be no evidence that Chavez took advantage of that opportunity.

On the other hand, she also apparently did not offer to help the woman by shepherding her through the paperwork necessary to work legally in the United States. That failure will be a much larger issue because Chavez is seeking confirmation for her role as leader of U.S. labor policy, which is very closely linked to immigration policy. Although immigration is legally governed by the state department, the concern uppermost in many Americans’ minds is its effect on jobs.

Conventional wisdom is that immigration should be allowed only at a level that will not take jobs away from American citizens and others already in this country. The manner in which Chavez seeks to provide an adequate labor pool without crowding citizens out of the job market may become more controversial if this economic "cooling trend" raises unemployment significantly. Right now, jobs are going begging, particularly those jobs filled by workers from Latin America. Most analysts acknowledge that even in times of recession, Americans are not standing in line to perform such tasks. If Americans are unemployed while illegal immigrants work, though — even in jobs Americans have never seemed to want — that’s going to be a problem for Chavez and Bush.

It already is a problem between the Bush administration and organized labor. The AFL-CIO, whose president John Sweeney has called Chavez’ nomination "an insult to American working men and women," issued a statement on Sunday saying that, "Unfortunately, her explanation sounds too much like the explanation of employers who have tried to skirt the law by saying that individuals are not their employees."

That raises another issue: skirting the law, which Chavez certainly knew. It’s entirely possible that immigration law is unfair or unrealistic and should be changed. Would Chavez address the labor components of such change — including legal protections for undocumented workers — in her position? Would she advocate looking the other way, as she herself seems to have done? Organized labor within the United States is not likely to be a party to that.