The future remains uncertain for 11 million people living illegally in the U.S. Though immigration reform seems closer than it has ever been before, can Washington and the Obama administration effectively repair 30 years of broken policies? (The Fold/The Washington Post)

As the full Senate engages in intensive deliberations over a landmark immigration bill this week, proponents are scrambling to maintain crucial bipartisan support in the face of Republican demands to strengthen border security.

GOP critics in both chambers of Congress have denounced the comprehensive Senate proposal for failing to secure the U.S. border with Mexico before allowing up to 11 million undocumented immigrants to gain legal status. They have vowed to push an array of amendments aimed at forcing the government to implement stricter border controls.

But Democrats, along with some Republican allies, fear that many of the proposals are too onerous and are aimed primarily at delaying — or ultimately preventing — illegal immigrants from gaining a green card or citizenship.

President Obama said in his weekly radio address Saturday that opponents will “try to stoke fear and create division. They’ll try to play politics with an issue that the vast majority of Americans want addressed. And if they succeed, we will lose this chance to finally fix an immigration system that is badly broken.”

Immigration advocates have said they will withdraw support for the bill if the border control “trigger” that would allow illegal immigrants to earn permanent legal status is made too difficult. Negotiations over border control could be pivotal in coming weeks as Senate backers of the plan aim to win more than 60 votes to guarantee passage.

“We are willing to toughen the border. Many of our colleagues believe that’s important,” said Sen. Charles E. Schumer (D-N.Y.), a leading member of the group of four Democrats and four Republicans that developed the legislation. “But without forsaking our principles. One principle is that the trigger has to be both achievable and specific.”

Over the past two weeks, since the Senate Judiciary Committee voted 13 to 5 to send the bill to the chamber floor, senators on both sides of the aisle have been developing more amendments and negotiating behind the scenes.

Though Schumer has expressed confidence that the bill could ultimately earn more than 60 votes, Sen. Marco Rubio (R-Fla.), another key member of the bipartisan group, has warned that it will not pass the Senate without stiffer border control measures.

Rubio has been discussing ideas with GOP colleagues and is considering offering an amendment to address their concerns, aides said. Though they would not discuss details, the aides said Rubio’s plan would likely include provisions allowing Congress to set specific border metrics for the Department of Homeland Security to achieve before the permanent legalization of undocumented immigrants can begin.

“We have a national security obligation to this country to ensure that we secure our borders for our own sovereignty, for our own security and to ensure that there isn’t another wave of illegal immigration in the future,” Rubio said during an interview last week with the EWTN Global Catholic Network.

Rubio aides said that if he offers an amendment it would be complementary to an amendment that has been developed by Sen. John Cornyn (R-Tex.), who voted against the bill in committee.

The bill, in its current form, requires DHS to submit a border security plan to Congress within six months, increase the number of customs agents and apprehend 90 percent of those trying to cross illegally over the U.S.-Mexico southwest border.

Up to $7 billion would be authorized to achieve those goals over the next decade. But illegal immigrants would be allowed to gain green cards after 10 years and citizenship after 13 years even if those provisions have not been fully met.

Cornyn has authored an amendment that would require DHS to achieve monitoring of 100 percent of the border, implement a biometric system to track foreigners entering at all air and sea ports and block illegal immigrants who have been convicted of serious misdemeanors from gaining legal status.

Under Cornyn’s plan, undocumented immigrants would not be able to gain green cards until the provisions are met in full.

“Unless these flaws are corrected, I will not be able to support the legislation,” Cornyn wrote in an op-ed in the Dallas Morning News last week.

Immigration advocates, however, have said the Cornyn amendment would not provide enough certainty for illegal immigrants, potentially creating indefinite delays for their path to citizenship. They view Cornyn’s move as a “poison pill” expressly intended to break the bipartisan alliance and kill the bill.

“The problem you’ll have if you try to enhance border security in an unachievable way and tie it to the path to citizenship, I think the deal falls apart,” said Sen. Lindsey O. Graham (R-S.C.), a member of the bipartisan group.

The group plans to meet each day of the lengthy floor debate to discuss pending amendments and come up with ways to lure Republican votes while also keeping the core of the bill’s principles intact.

Amendments are expected to come from both sides of the aisle. Liberals will likely push to insert language recognizing same-sex immigrant couples in the legislation. Sen. Richard Blumenthal (D-Conn.), has said he will propose amendments making it easier to track attempted gun purchases by temporary visa holders, most of whom are barred from buying guns.

Graham said he viewed Rubio’s comments on border security as efforts to improve the bill and pick up support, not abandon the effort. Many Democrats believe Rubio’s effectiveness as a conservative supporter of the bill is boosted by the impression that he is fighting on behalf of changes sought by Republican-leaning groups.

“I won’t abandon this issue until it’s done, until we get a bill passed,” Rubio told reporters last week.

Rubio’s moves also could foreshadow what happens in the House, where another bipartisan group has failed to come to an agreement on a comprehensive immigration plan. Key hurdles have been a new visa program for foreign low-skilled workers and disagreement over whether illegal immigrants would be required to buy health-care insurance, aides said.

Last week, a key member, Rep. Raul R. Labrador (R-Idaho), quit the group out of frustration with the lack of progress, leaving it with seven members.

Senate leaders said they hope to vote on the legislation before July 4, while House Speaker John A. Boehner (R-Ohio) has said he hopes to have some kind of legislation voted on in the House by August. That could set up a joint-chamber conference in the fall aimed at hammering out a compromise.