“Illegal immigrants are imbedded in our nation, so allowing them to apply for a work visa would be a good way to draw them in and set a path for them to become legal,” said Mr. Nuñez, whose family came from Puerto Rico. “If they have been working here and are law-abiding and can contribute to our country, they should be allowed to stay and become citizens.”

Most of those polled agreed that illegal immigrants should eventually be allowed to apply to become American citizens. But 59 percent said that former illegal immigrants should be considered for citizenship only after legal immigrants who have played by the rules.

Under the Senate bill, illegal immigrants would have to wait eight years before they could become permanent residents and at least 13 years to become citizens.

Two-thirds of Americans in the survey favored creating a guest worker program for future immigrants. The bill would create a temporary worker program in which immigrants would come for three stints of two years each, going home for one year between each stint and returning home for good after the third.

More than half of those who favor the guest worker program say the workers should be allowed to apply to become permanent immigrants and eventually American citizens if they maintain a strong work history and commit no crimes. About a third of those who favored the program disagree, saying guest workers should be required to return home after their temporary period.

The bill does not include a path to citizenship for guest workers. In the debate, Democrat senators have assailed the temporary worker plan, saying it would create an underclass of easily exploited low-skilled workers. On Wednesday, senators voted to cut back the number of guest workers to 200,000 from the 400,000 proposed in the bill.

The bill also calls for reinforcing the borders, cracking down on employers who hire illegal immigrants and eliminating the backlog of visa applications from aspiring legal immigrants. In the poll, 75 percent of those who responded favored tougher penalties for employers of undocumented workers, and 82 percent said the federal government should do more to reinforce the border. But only 15 percent of respondents favored fences as the main method to reduce illegal border crossings.