They say any bill that even hints at amnesty or legalization for millions of illegal immigrants already living and working in the United States is dead before it ever makes an appearance in a congressional committee.
A path to citizenship is "what has doomed all immigration legislation in the last two administrations," California Republican Dan Lungren said during a recent House hearing on immigrant agricultural workers.
The agricultural workers' bill discussed during that hearing, which first was proposed in the last Congress, isn't likely to be revived.
"It's not going to pass," Lungren said matter-of-factly while taking testimony on the visa program that helps supply temporary workers to agricultural businesses. "And it's not going to pass because it has, frankly ... a path to citizenship."
Rep. Lamar Smith, a Texas Republican who chairs the House Judiciary Committee, said immigration reform proposals that offer a path to legal status are tantamount to amnesty.
"I think most members of Congress and most Americans don't want to reward lawbreakers and don't want to give them amnesty," Smith said Tuesday as Obama held his White House meeting.
The failure of the DREAM Act is a key example. The bill would have provided a path to legal status for law-abiding young people brought to the United States as children who either plan to attend college or join the military.
"Remember, in the last Congress, the Democrats had large majorities and weren't able to pass the comprehensive amnesty bill," Smith said. "I don't think that bipartisan resistance to mass amnesty has (abated)."
Obama also promised to continue working to build a bipartisan consensus around immigration and said he would lead a "civil debate" on the issue in the months ahead, the White House said. But he also said he will not succeed if he alone is leading the debate.
"The president asked the group to commit to moving forward to keep the debate about this issue alive, to keep it alive in the sense that it can get before Congress, where the ultimate resolution of it will have to be obtained," said Bill Bratton, the former police chief in Los Angeles and New York City. "The idea being to go out into our various communities and to speak about the issue."
According to a statement from the White House, "The president urged meeting participants to take a public and active role to lead a constructive and civil debate on the need to fix the broken immigration system. He stressed that in order to tackle the issue successfully they must bring the debate to communities around the country and involve many sectors of American society in insisting that Congress act to create a system that meets our nation's needs for the 21st century and that upholds America's history as a nation of laws and a nation of immigrants."
For his part, Smith said he thinks the Obama administration should first secure the U.S.-Mexican border and put a greater emphasis on rooting out illegal workers and the businesses that hire them.