Three years after efforts by Congress to reform the immigration system went down in flames, the issue is slowly re-emerging on the national stage, as two senators from the opposite sides of the political aisle work on crafting another bill.

Sen. Chuck Schumer, D-N.Y., chairman of the Immigration Subcommittee of the Judiciary Committee, and Sen. Lindsey Graham, R-S.C. are set to appear Thursday at the White House for a meeting with President Obama in which they are expected to seek his guidance on charting a path forward.

The reform effort blew up in 2007 after more than a year of work when Republican critics branded the effort as "amnesty" and the tide of public opinion turned strongly against the bill.

Graham, in fact, was booed at a Republican gathering in his state in 2006 for his work on comprehensive reform with Ted Kennedy and John McCain. Sen. McCain is conspicuously absent from the current talks; Graham remains at the table as the lone Republican supporter.

Schumer said comprehensive immigration reform is closer to reality than it appears.

"We only have a couple more things to get done," he said Wednesday. "They're hard. One is to get another Republican on the bill; one is to finally deal with the issue -- to get business and labor on the same side on future flow on low-wage workers."

A senior Senate Democratic leadership aide close to the debate said of the White House meeting, "They're giving the president an update on where they stand, but they're also reaching out to get support on securing that second Republican and for help in dealing with business and labor."

Organized labor, in 2006 and 2007, fought any robust guest worker program, also called "future flow," as Kennedy's bill sought to create with the support of President George W. Bush.

Though a GOP aide with knowledge of the process told Fox News the effort is far from complete, Schumer maintained, "We're getting real close. I'm optimistic."

Immigrant rights groups have pushed to get a bill, even without another Republican joining, but Schumer said Wednesday, that's not going to happen. "Senator Graham has been very good and generous and courageous in helping us move that bill forward. ... He has always said he wants a second Republican."

Anxious to avoid the explosive failure of the last effort, Schumer said emphatically, "We will not pass an immigration bill unless it's bipartisan. Everyone agrees with that."

Schumer said it has been a tough slog to get a second Republican, particularly since pro-reform GOP Sen. Mel Martinez of Florida, himself a Cuban immigrant, recently retired. "It's been difficult finding a second Republican," he said. "We have four or five prospects we're working on now. But if we can't, we'll have to cross that bridge when we come to it. But we're not giving up."

One Republican senator who is thought to be in play is the newest member of the body, moderate Sen. Scott Brown of Massachusetts. While Brown didn't slam the door on a compromise, he did not sound anxious to deal with this issue now with the unemployment rate hovering near 10 percent.

Brown told Fox News he has not yet been contacted by either Schumer or Graham, but he is willing to take a look at their bill, even though he suggested now is the time for Congress to focus on jobs, not immigration.

"We're doing health care, maybe immigration. The thing I haven't heard enough about is jobs, job creation. It's nonexistent. I think that's a mistake." Brown said, "Right now, people need jobs, period."

When asked what must be in any immigration reform bill, Brown said, "You need a strong border enforcement. You need a strong E-verification. I...have always felt that part of the problem is that we haven't provided the proper resources for people to be processed quickly enough. And when you have people waiting in line six, seven, eight, nine years in some instances, it's a disincentive to (immigrate) legally...In terms of allowing people to step ahead of the people who are trying to do it legally, I have a real problem with that."

In fact, that very issue is what tripped up the earlier effort, what's commonly referred to as "the path to legalization." The Kennedy-McCain bill laid out a series of hurdles for potential citizens to clear, a six-year process in which workers who were in the country illegally could apply for a six-year "conditional non-immigrant visa." At the end of that period, a visa holder could apply for legal permanent residence if the person paid a $1,000 fine, passed a background check, and demonstrated an effort to learn English and civics.

Critics called this "amnesty," and at the time, the House, then run by Republicans, passed a narrow, border security-only measure, and left Senate Republicans who might have supported Kennedy-McCain holding the bag. In the end, that handful of Republicans bolted and the bill went down in flames.

It is not likely the crowded Senate calendar can withstand another controversial debate this year, but Sen. Majority Leader Harry Reid, D-Nev., continues to list it among his top priorities to tackle this year. Though Sen. Dick Durbin, D-Ill., the No. 2 Democrat in the chamber, did not sound quite so sure, "Depends on support we get from the other side...I support comprehensive reform, but I'm going to leave that to Chuck."