US:US president George Bush has appealed to Democrats and Republicans in Congress not to give up on reforming America's immigration system because of the emotional political issues involved.
Speaking in Yuma, Arizona, on the US border with Mexico, Mr Bush said that any reform must allow many undocumented immigrants now in the US to remain in the country legally.
"Illegal immigrants who have roots in our country and want to stay should have to pay a meaningful penalty for breaking the law, and pay their taxes, and learn the English language, and show that they've worked in a job for a number of years. People who meet a reasonable number of conditions and pay a penalty of time and money should be able to apply for citizenship. But approval would not be automatic, and they would have to wait in line behind those who played by the rules and followed the law," he said.
Senate majority leader Harry Reid has set aside two weeks in May to debate an immigration reform Bill but Senator Edward Kennedy said this week that no legislation could succeed without substantial Republican support.
Mr Bush has said he wants Congress to pass an immigration Bill by August, although he has given few details of the formula he favours.
Mr Kennedy plans to revive a Bill that was approved by the Senate judiciary committee last year but later amended on the floor of the Senate. The Bill would allow most illegal immigrants to remain in the US and work legally. They would have to pay a fine and learn English but would eventually be allowed to apply for citizenship.
Senate Republican leaders insist that illegal immigrants must first go home briefly before returning to the US legally and that fines should be substantial. Many Republicans are also determined that guest workers should not be allowed to bring their families to the US.
Some legislators are looking at a proposal to give guest workers a renewable, three-year visa, for which they would have to pay $3,500 every three years. Currently illegal immigrants seeking to stay in the US permanently would have to pay up to $10,000.
In the House of Representatives, Speaker Nancy Pelosi says she will not introduce a new immigration Bill unless it has the support of at least 70 Republicans. Democrats are under pressure from Hispanic voters to take action on immigration but trade unions are insisting that any new Bill must include a mechanism to protect wage levels.
Republicans are deeply divided between pro-business advocates of immigration reform and those who want to seal the US border with Mexico and oppose what they view as an amnesty for lawbreakers.
A wave of raids on businesses that employ illegal immigrants has seen 18,000 people arrested in recent months and the number of people caught trying to enter the US illegally has fallen. The Irish Lobby for Immigration Reform, which campaigns for Irish undocumented immigrants in the US, is holding a rally in Dublin next Saturday.