The US Senate has voted to revive discussion of a wide-ranging plan for immigration reform.
The bill is supported by President George W Bush, who has said the issue is at the top of his domestic agenda.
The legislation would bring in tighter border controls but offer 12m illegal immigrants a path to citizenship.
Efforts to secure Congressional approval have been stalled for many months, because of opposition from both Republicans and Democrats.
Senators voted 64-35 to resume debate on the compromise legislation, which was put together by both parties and the White House.
However, it faces a bumpy ride in the next few days as leaders from both parties try to push it through before Friday, when the Senate will break for a week-long recess, correspondents say.
Senate leaders have added an extra $4.4bn (£2.2bn) funding for border security in an attempt to overcome Republican opposition.
Democratic Senator Edward Kennedy, one of the backers of the bill, said the vote to revive debate “was a major step forward for our national security, for our economy and for our humanity”.
However, Republican Senator Jim DeMint warned the measure would continue to face stiff opposition from some senators, many of whom are under pressure from conservative voters to block its progress.
“The momentum against this bill is growing all across the country,” he said.
The bill faltered earlier this month when it failed to win the backing of enough Republicans to move to a final vote.
Mr Bush responded with a personal appeal to his party to back the legislation, attending a Republican policymakers’ luncheon on Capitol Hill to press his point.
Speaking ahead of Tuesday’s vote to resume debate, he urged Congress not to miss a “historic opportunity” to reform a system that was not working.
The deadlock followed a series of amendments to the proposed bill, which undermined the fragile bipartisan compromise.
Illegal immigration is among voters’ top concerns and is set to be a key issue in the 2008 presidential poll.
Under the proposed Senate bill, illegal immigrants would be able to seek a renewable “Z visa” after paying a $5,000 (£2,530) fine.
They could ultimately be placed on the path to permanent residency—a process that could take several years.
The bill also set out a “points system” that emphasises immigrants’ education, language and job skills over family connections in awarding green cards.
But these measures would not come into force until 18,000 new border guards are deployed, the fence with Mexico reinforced and hi-tech surveillance put in place.
Some critics have labelled it an “amnesty” for those who have illegally entered the US.
Others have argued that its guest worker programme threatens US workers, or that it will create an underclass of cheap foreign labourers.