Still, in a sign of the ambivalence among voters about an emotionally charged issue, a strong bipartisan majority, 60 percent, favors allowing illegal immigrants who have not committed crimes to become citizens if they pay fines, learn English and meet other requirements.
Those crosscurrents create treacherous political waters for the major presidential candidates in both parties, many of whom have tended to avoid spotlighting the issue.
During Tuesday's radio debate among Democrats, the candidates were asked
if citizens should turn in someone they know to be an illegal immigrant.
Most said no.
In other settings, however, several have been talking a tough line on issues such as denying driver's licenses to illegal immigrants.
Some poll respondents, in follow-up interviews, expressed frustration that the candidates have not been more forthright in addressing immigration-related issues.
"I don't know what the answer is, but I don't think the candidates know what the answer is either," said Lodie Lambright, a retired state government worker in Rhode Island.
The survey, conducted under the supervision of Times Poll Director Susan Pinkus, was based on interviews from Friday through Monday of 1,245 registered voters. The margin of sampling error was plus or minus 3 percentage points.
The poll indicates that illegal immigration is not the most important issue voters have on their minds, but that most people view it as a key concern.
Asked what problem is a top priority for presidential candidates to address, 15 percent said illegal immigration, the fifth most-mentioned topic behind the war in Iraq, the economy, protecting the country from terrorist attacks, and health care.
Asked how much of a problem illegal immigration is, 81 percent of voters said they considered it important, including 27 percent who said it was one of the most pressing problems facing the country.