GOP negotiators of an immigration reform bill are crafting a large border security amendment with mandatory, immediate funding that they hope will assuage concerns of both Republicans and Democrats, FOX News has learned.

The senators are looking at a way to please conservatives who are skeptical Congress will ever fund the bill's border security provisions, as well as keep Democratic negotiators on board in a last ditch effort to save the comprehensive reform bill.

It is a political tightrope fraught with peril, but the members know they need more Republican support to break through the logjam.

South Carolina Sen. Lindsey Graham, a principle author of the amendment with Republican Sens. Jon Kyl and Mel Martinez, says his amendment is designed to be "a confidence builder" to address members' concerns that ramped up border security provisions in the bill won't, in the end, get funded.

Graham hopes to provide $4.4 billion the day the bill is signed, through an estimate in fees and fines in the current immigration bill, to be used to beef up all the border security measures in the bill, with an additional $800 million for further measures, taking from measures put forward last year by New Hampshire Sen. Judd Gregg who called for more investment in capital infrastructure, like unmanned aerial vehicles and new Coast Guard boats.

Graham said this $4.4 billion would be borrowed from the Treasury and repaid once the fines and fees from the bill are collected, like the $5,000 fine each illegal has to pay for a work visa, called a "Z visa." Graham said it would be better to do it this way, rather than an emergency funding bill, which goes directly to increasing the deficit.

"If you put the money into this bill, it goes a long way toward building confidence," Graham predicted.

Visa overstays will become a crime under the Graham-Kyl-Martinez amendment, and repeat offenders would face mandatory jail time, deportation, and a ban from ever re-entering the U.S. It is unclear what Democratic negotiators like Sen. Edward Kennedy will do. He has not supported this kind of stiff penalty in the past.

Graham would also forever bar employers from participating in the guest worker program if they have violated immigration laws repeatedly.

It is unclear if this approach can work. "They tell me it can be done," Graham said, but he added that his staff is investigating this now.

The negotiators met tonight to lay out amendments Democrats and Republicans must have. The intention is to have a list of "less than 20," according to aides, and this final list would be showed to Majority Leader Harry Reid Wednesday.

Earlier today, President Bush told Republican lawmakers on Capitol Hill that failure to adopt a new bill will leave in place an "unacceptable" status quo.

Some of the lawmakers Bush met with "believe that we need to move a comprehensive bill, some don't. I understand that. This is a highly emotional issue," the president said after the meeting.

"We have got to convince the American people that this bill is the best way to enforce our borders. I believe without this bill, it's going to be harder to enforce the border. The status quo is unacceptable. And I want to thank those senators on both sides of the aisle that understand the time is now to move a comprehensive piece of legislation and the White House will stay engaged," Bush said.

Sen. Trent Lott said lawmakers offered several questions and comments to the president, who was anxious to work with the Senate to get the job done.

"The president made it clear to me and to others that he does not want just any bill, won't sign a bad bill, but he thinks this is an issue that needs to be addressed for the benefit of our country,” Lott, R-Miss., said. “I hope that the majority leader will work with us in a way to get it up in a fair process to move it forward.”

“We’ll move on to immigration when they have their own act together,” Senate Majority Leader Reid said in response.

Nonetheless, several Democrats and Republicans expressed their hope of saving the bill after the Senate voted 45-50 last Thursday to block an end to debate and prevent the Senate from moving to final arguments before a vote on passage.

Opponents said the bill still offers "amnesty" to millions of people who defied U.S. law and crossed the borders without permission. Still, most lawmakers recognize that many of those immigrants have since integrated into the workforce and many are raising their families in the U.S.

They have for the most part dropped calls for these illegals to be removed from the country, though the legislation does require heads of households seeking permanent resident worker status to "touch back" to their home countries to apply for legal work papers.

At the same time, lawmakers also recognize that the status quo cannot be sustained, with an estimated average 54,000 illegal immigrants entering the U.S. each year.

"We think that there's going to be a strong support on final passage when the bill is brought up and finally they've concluded the debate," White House spokesman Tony Snow said before the president's meeting. Snow noted that Republicans killed the bill only after Democratic leaders denied them the opportunity to amend the legislation.

Anticipating Bush's arrival, Kennedy said he was hopeful the president, who has made immigration reform his top domestic priority, would help make the difference.

"Like the president, many of us are very determined to get the job done and get it done now. The center is holding together: last night we met to discuss the options for moving it forward and today we'll continue that work. We share the sense of urgency that this important issue deserves," Kennedy said in a statement.

Kennedy's statement follows a letter to Bush penned by Senate Democratic leaders urging him to lean on Republicans to back the measure.

"It will take stronger leadership by you to ensure the opponents of the bill do not block its path forward," the letter said. "Simply put, we need many more than seven Republicans" to support the bill.

But Republican opponents sent their own letter to Bush on Tuesday, urging his administration to follow through with the provisions of last year's immigration reform bill, which called for hundreds of miles of fence to be built along the U.S.-Mexico border.

"We respectfully ask that your administration enforce the border security laws that have already been authorized by Congress regardless of whether the Senate passes the immigration reform bill," the letter from nine Senate Republicans reads.

"The bill assumes that several critical border security benchmarks can be achieved within 18 months. These security triggers are already authorized under current law and can be completed without the immigration bill," the letter continues.

According to a FOX News-Opinion Dynamics poll released last week, a majority of those surveyed — 58 percent — said they want the federal government to enforce existing border security laws. Thirty-four percent said the entire immigration process needs to be scrapped and reworked. But support for allowing illegal immigrants to stay in the United States is 67 percent when conditions of paying taxes and obeying the law are met.

Click here to see the poll results.

FOX News' Trish Turner and The Associated Press contributed to this report.