WASHINGTON (AFP) - The White House warned Republican lawmakers on Wednesday not to block a comprehensive immigration reform bill just to appease "far right" conservatives who are after their jobs.

The warning came amid growing signs that a bill to offer a path to citizenship for 12 million undocumented immigrants, which easily passed the Senate, may wither and die in the Republican-led House.

White House spokesman Jay Carney acknowledged that passing the bill, which would form a key plank of President Barack Obama's legacy, was "an uphill battle" but said the measure enjoyed widespread support.

"It cannot be acceptable broadly and in the long term that immigration reform would be blocked because some minority of House Republicans is concerned about a primary challenge from the far right," Mr Carney said.

"That's not a good argument. It's not a good argument politically. It's certainly not a good argument economically." National Republican leaders recognise that scuppering immigration reform could be politically disastrous, given its importance to the increasingly important Hispanic voting bloc.

But many House Republicans, with few Hispanics in their districts, have little incentive to back a bill fiercely condemned by many conservatives as an "amnesty."

The White House, which stayed in the background for much of the Senate debate in immigration last month, is trying to crank up the pressure on House Republicans to force them to pass the bill.

In a report issued on Wednesday, the administration argued that the bill would grow the economy by 5.4 percent due to an enlarged labor force and that it would see wages rise by 0.5 per cent.

It said the bill would also cut federal deficits by nearly US$850 billion (S$1.07 trillion), while the federal debt would drop three percent as a share of the economy by 2023.

Republican leaders have signaled they will not bring up the massive Senate bill for a debate or a vote in the House. But they have said they may bring up measures conservatives do favour, such as border security, piecemeal.

They have also made it clear that House Speaker John Boehner will not seek to build a coalition to pass the legislation among more moderate Republicans and minority Democrats.

The standoff will pit House Republicans against influential members of their party in the Senate, including Marco Rubio, who was instrumental in framing the bill and is a possible 2016 presidential candidate.

House Republicans gathered on Wednesday for what was likely to be a tense meeting on the way forward on immigration with Boehner under rising political pressure from conservatives to halt the bill's progress.

Democrats meanwhile touted recent polls showing that a majority of voters in some key districts back the Senate legislation and that Republicans who oppose it could be hurt in mid-term elections in 2014.

Public Policy Polling director Tom Jensen said that in surveys of seven congressional districts with Republican incumbents and a history of close elections, between 61 and 69 per cent of voters supported the Senate bill.

"What we found is that voters are just much less likely to vote for somebody if they vote against immigration reform," Public Policy Polling director Tom Jensen told reporters.

Mr Brad Woodhouse, president of pro-Obama grass roots group Americans United for Change, was more blunt.

"Their majority is in jeopardy if they screw this up," he said of the challenge facing Republicans.

"There may be nothing more convincing to Republicans who have repeatedly opposed immigration reform in the past... than the political price they'll pay if they fail to pass immigration reform now."