Washington ? Senate Majority Leader Bill Frist said Sunday he wants a full Senate vote on an immigration bill this week and believes that urgent action is needed despite sharp divisions over whether proposed legislation would amount to amnesty.

“There are 3 million people every year coming across our borders illegally. We don’t know who they are; we don’t know what their intentions are. We absolutely must address it,” said Frist, a Tennessee Republican. “I hope by Friday that we will have a bill on the floor that is comprehensive.”

The Senate Judiciary Committee last week approved a bill aimed at strengthening enforcement of U.S. borders, regulating the flow into the country of so-called guest workers, and determining the legal future of the illegal population scattered across all 50 states.

The Senate version, which passed 12-6 in committee and was broadly endorsed by President Bush, goes further than a House bill that imposes criminal penalties, proposes building a fence along the borders and is limited to enforcement.

Meanwhile, a poll released Sunday showed that Americans are divided on immigration issues. More than half of those questioned are open to allowing undocumented workers to obtain some temporary legal status so they can stay in the United States.

At the same time, people doubt that erecting a fence along the U.S.-Mexico border could help to fix such a complex and enduring problem, the AP-Ipsos poll found. Two-thirds do not think it would work.

“You can’t go and round up 11 million people and ship them out of the country,” said Robert Kelly. The Chicago lawyer is among the 56 percent of Americans who favor offering some kind of legal status.

A smaller but still significant share – 41 percent – opposes offering any kind of legal status.

“Illegal is criminal,” said Louella Kelly, a 65-year-old grandmother from Round Rock, Texas.

She said her 16-year-old granddaughter has had a hard time finding part-time work because of all the jobs taken by those who are illegally in the country. “If we’re going to give them amnesty, then why don’t we give amnesty to all the people who break out of jail?”

The AP-Ipsos survey of 1,003 adults was conducted Tuesday through Thursday. The survey had a margin of error of plus or minus 3 percentage points.