UKIP leader Nigel Farage has called for immigrants to be barred from receiving any benefits until they have been resident in the UK for five years.
He also suggested they should not be eligible for tax credits.
It comes as a survey suggests 77% of Britons want to see immigration cut.
The coalition brought in a three month ban on EU citizens getting out-of-work benefits ahead of work restrictions being lifted for Bulgarians and Romanians on 1 January.
But Mr Farage, whose party fought the last election on a policy of halting immigration for five years, said the government should go much further.
He said the cost of migrants claiming in-work welfare payments, such as child benefit, housing benefit and tax credits, had not been factored in to the government's calculations.
"We must be completely mad, as a country, to be giving people from Eastern Europe in-work benefits," he told BBC News.
And he said lower economic growth was a price worth paying for cutting immigration.
"Even if I thought, which I don't, there was an economic benefit to mass immigration some things are more important than money, namely the shape of our society and giving our own youngsters a chance to work."
London Mayor Boris Johnson also weighed in to the debate, suggesting the ban on EU citizens claiming benefits should be two years.
Labour said it supported the government's three-month ban, which it said was "reasonable and achievable".
Downing Street said withholding benefits from migrants for longer periods may be illegal.
"We are doing all that we can within the law," said a No 10 spokesman.
Downing Street also confirmed ministers were examining measures to curb the ability of migrants to claim child benefit for children in their native countries.
The British Social Attitudes Survey suggests more than three-quarters of Britons want to see a cut in immigration - and 56% want to see a major crackdown.
Almost half of those surveyed, 47%, thought immigration was bad for the economy, and among the 31% of respondents who said it was good for the economy, half wanted to see immigration reduced anyway.
The figures are revealed in a BBC Two documentary called The Truth About Immigration, to be broadcast later on Tuesday.
Business Secretary Vince Cable tells the programme the government's target of cutting net migration to below 100,000 by 2015 is "not helpful" and will almost certainly not be achieved.
Mr Cable, who has sought to distance himself from the net migration target in the past, calling it a Conservative and not a coalition policy, said politicians on all sides must be "practical" and accept that net migration cannot be controlled.
"It involves British people emigrating - you can't control that. It involves free movement within the European Union - in and out. It involves British people coming back from overseas who are not immigrants but are counted in the numbers," he says.
"Setting an arbitrary cap is not helpful. It almost certainly won't achieve the below-100,000 level the Conservatives are setting - so let's be practical about it."
Labour said the "gap between the government's rhetoric and reality on immigration is continuing to undermine public confidence".
Shadow immigration minister David Hanson said Mr Cable should toughen up enforcement of the minimum wage and prevent employment agencies recruiting solely from abroad.
David Cameron promised to cut net migration - the difference between the number of people coming to live in the UK and those emigrating - from more than 250,000 a year to less than 100,000 by the next election in 2015.
After some initial success, the latest figures show net migration is on the rise again, going up from 167,000 to 182,000 a year, largely because fewer Britons were emigrating to eurozone countries.
Asked last month if that meant it would be impossible to meet his target, Mr Cameron said: "'I don't accept that."
"If you take the whole three-year period [since the election], net immigration is down by around third."
He said some measures the government had taken, such as closing "bogus" colleges and tightening up the rules on family reunion, would take time to have an impact.
In Nick Robinson's documentary, former Foreign Secretary Jack Straw says the Labour government of which he was a prominent member "got it wrong" on immigration, "and I deeply regret it".
Labour MP and former Home Secretary David Blunkett adds: "We didn't spell out in words of one syllable what was happening, partly because of a fear of racism."
Nigel Farage tells the programme: "They tried to rubbish us, they tried to say that anybody that dared to talk about this subject was necessarily a bad person and racist, that was what they tried to do and actually this has been going on ever since [Enoch] Powell's speech."
In the so-called "rivers of blood" speech, made in 1968, Mr Powell said Britain's immigration policy was like watching a nation "heaping up its own funeral pyre".
He was sacked from the Conservative shadow cabinet by party leader Edward Heath, who said it was "inflammatory and liable to damage race relations".
Asked whether he thought Mr Powell had been right, Mr Farage says: "He was right for the wrong reasons. He was wrong in the sense that he felt that black and white would find it difficult to mix, but unfortunately he's been proved to be right because the sheer numbers that have come into Britain have led to segregation."
BBC political editor Nick Robinson says all political parties now "promise to control" immigration because they are "acutely aware of the high level of public concern" about it.
In the programme, he looks back to a civil service paper published in 2001 which examined the economic and the social impact of immigration.
The paper concluded that there was "little evidence that native workers are harmed by migration".
Its author, former Cabinet Office economist Jonathan Portes, said: "I think politicians do have to say to individuals who are negatively affected, and let's face it there will be some: 'Yes, we're doing this for the good of our country, and yes you may lose out, but ultimately we still have to do this.'
"Just as we said to the coal miners 30 years ago: 'Sorry we can get our coal a lot cheaper abroad. We can't afford to keep on propping you up.'"
The Truth About Immigration is to be broadcast on BBC Two at 21:30 GMT on Tuesday, 7 January.