NEW York Mayor Rudolph Giuliani had it right. Depriving illegal immigrants of public education and public health services would be morally and fiscally devastating to communities like his. Thousands of kids out on the streets is a much more worrisome prospect than thousands sitting at desks in classrooms. The chances of the former happening, however, are not great. Though many of those campaigning in Washington and in the states for immigration reform might like to see illegals stripped of such benefits as public schooling, the legal hurdles to such moves are high. The US Supreme Court ruled in 1982 that immigrant children, even if their parents are in the country illegally, are entitled to a place in the public schools. The single biggest effort to turn that decision around, California's Proposition 187, has been blocked by legal challenges since its passage last November. Mayor Giuliani's concern springs from the efforts of fellow Republicans in the US House of Representatives to institute far-reaching changes in immigration policy, including tight restrictions on access to public services. Policy changes are both needed and imminent, impelled by a combination of the public's disgust with what it views as the failures of the present system and politicians' awareness that this can be a vote-getting issue. Also influential are the findings of the bipartisan US Commission on Immigration Reform, which has recommended sharp reductions in legal immigration, as well as ways to get at the problem of illegal entrants. Aside from the legal barriers, the type of policy changes that alarm Giuliani - specifically barring access to public education - are not part of the program of thoughtful reformers such as Rep. Lamar Smith (R) of Texas, a House leader on this issue. They recognize both the moral and practical problems inherent in such measures. By focusing on the education and health care areas, which raise the largest ethical and humanitarian concerns, the mayor may have been playing to New York's substantial immigrant constituency. Still, his voice joins many urging the country to be careful as it goes about immigration reform. Illegal immigration has to be dealt with, but punitive measures that target children, and indirectly the communities they live in, aren't the answer. The reason the desperately poor from Mexico and other lands uproot themselves is economic - they come in search of jobs, not food stamps or educations. And the job site is where enforcement has to center. Proposals for electronic verification methods that can quickly check on the authenticity of a Social Security number, for instance, are probably what's needed. The process would be much like a store clerk checking a credit card. The US has a right to monitor those who cross its border and send back those who break the rules. But it has to exercise reason and compassion - not anger and emotion - in doing so. The job site, not the public school, is the place to focus efforts to identify illegal immigrants.