The poll also found stiff resistance to allowing illegal immigrants to pay discounted in-state tuition at public colleges: 12% of those surveyed -- including 20% of Democrats and 6% of Republicans -- supported that idea.
However, some of those polled saw a humanitarian need to provide emergency healthcare, education and other basic services to illegal immigrants, especially to their children.
"You don't want to see a child go hungry or go ill," said Beverly Taylor, a retired postal worker in Indiana.
Respondents were divided about the best solution to the problem, but a strong majority expressed support for a proposal discussed in Congress -- part of a package backed by President Bush -- that would create a pathway to citizenship for illegal immigrants already in the United States.
The plan, under which illegal immigrants could become citizens if they have no criminal record, register with the Department of Homeland Security, pay a fine, learn English and meet other requirements, was supported by 64% of Democrats and 62% of Republicans.
However, that plan died in Congress under withering fire from critics who called for the nation to tighten border security before considering more liberalized treatment of illegal immigrants.
And the plan has been little discussed by candidates on the presidential campaign trail -- even by Sen. John McCain (R-Ariz.), who was one of its leading proponents.
The poll suggests that neither party heads into the 2008 election with a decisive advantage on the issue, with Democrats having lost an edge they once enjoyed.
Those surveyed were evenly split on which of the two major parties would do a better job handling immigration: 31% chose Republicans and 30% picked Democrats. By contrast, a poll in June 2006 showed 34% preferred Democrats and 23% preferred Republicans.
Associate polling director Jill Darling contributed to this report.