Senators pushing a new immigration policy appealed Sunday to wavering supporters ahead of renewed debate on securing the borders and dealing with 12 million undocumented immigrants.

A fragile compromise was pulled from the Senate in early June, then resurrected after bipartisan negotiations with the White House. The bill awaits a crucial test vote this week. With several senators distancing themselves from the proposal, the outcome was too close to call.

"We'll see if between the two parties we have 60 votes" needed to keep the bill moving toward a final vote, said Sen. Dianne Feinstein, D-Calif.

The measure would tighten borders, require workplace verification and create a guest worker program. It also would lay out a way by which the estimated 12 million people illegally in the U.S. could gain legal status and work toward citizenship.

President Bush long has advocated an immigration overhaul. On Saturday, he urged lawmakers to "summon the courage" to support what could be the last major legislative achievement of his presidency. "The status quo is unacceptable," he said in his weekly radio address.

But he faces dissension from fellow Republicans who demand better border security and oppose any policy that suggests amnesty for undocumented immigrants.

Senate Republican leader Mitch McConnell, R-Ky., last week said his support for the bill hinges on the outcome of a series of amendments agreed to as part of the compromise to revive the legislation.

Sen. Trent Lott, R-Miss., who has faced critical ads back home over his support for the bill, said Sunday, "I'm not committed to voting for the final product. The wheels may come off. But I am committed to trying."

Democrats have taken hits from their normal allies, including labor and some Hispanic groups. They say the proposal is bad for workers or that provisions for obtaining visas place too much emphasis on skills, to the disadvantage of family ties.

"We know what they're against. What are they for?" asked Sen. Edward Kennedy, D-Mass. He noted that since the Sept. 11 attacks, there have been 39 hearings on immigration, 23 days of debate in the Senate and 52 amendments.

"We have a terrible problem in this country that demands an answer," he said.

But Sen. Jeff Sessions, R-Ala., a leading critic of the legislation, argued that support for the bill continues to plummet, both among senators thought to be behind it and among the public.

"We are going to use every effort to slow this process down and continue to hold up the bill," he said.

Senate passage would send the issue to the House, where Democratic leaders have promised to take it up at an early date. But the legislation also faces a tough road in the House. Many Republicans want tighter border security and opposing giving legal status to those who entered the country illegally.

Feinstein and Lott appeared on "FOX News Sunday" while Kennedy and Sessions spoke on "This Week" on ABC.