The US Senate has voted to revive discussion of a wide-ranging plan for immigration reform.
President Bush urged Congress not to miss out on a historic opportunity
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.
The bill faltered in the Senate earlier this month when it failed to win the backing of enough Republicans to move to a final vote.
Senators on Tuesday voted 64-35 to resume debate on the compromise legislation, which was put together by both Republican and Democratic leaders and the White House.
However, it faces a bumpy ride in the next few days as its backers 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.
Supporters of immigration reform have held a number of big rallies
Democratic Senator Edward Kennedy, one of the sponsors of the bill, said the compromise measure "may not be perfect, but it is the best opportunity we have to do something significant and substantial".
However, Republican Senator Jim DeMint warned the legislation 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.
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 new "Z visa" - which would allow them to stay in the country but must be renewed every two years - after paying a $5,000 (£2,530) fine.
To get the Z visa, they would have to pass a background check, remain employed and receive a tamperproof identity card.
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.