Not so fast, Mr. President.
They say any bill that even hints at amnesty or legalization for millions of undocumented 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.
"There are 7 million illegal workers in this country," Smith said. "I'd like to see those jobs go to American citizens and legal workers."
He also criticized the Obama administration for what he sees as a substantial reduction in workplace enforcement.
Immigration and Customs Enforcement, which is responsible for finding and removing undocumented immigrants and enforcing bans on employing them, has greatly reduced the volume of highly public raids that became an enforcement staple of the Bush administration. ICE has been relying instead on audits of paperwork employers are required to maintain that proves their workers are legal.
"It's premature to talk about anything other than enforcing the law and protecting jobs for American citizens and legal immigrants," Smith said.
Lungren and Smith said they do see a relatively promising future for a bill that would require all employers to use the government's employee verification program, E-Verify, and perhaps an improved guest worker program.
Despite what appears to be solid opposition to immigration overhaul bills, Rep. Zoe Lofgren, D-Calif., said she still sees hope for changes to what she describes as a broken system.
"Ultimately, the system will be reformed and the question is when and how much damage is the country going to have to go through," Lofgren said Tuesday.
Lofgren said she sees "big steps forward" in the future in the form of changes to immigration laws that affect immigrants married to U.S. citizens and a revamped DREAM Act, among others.
Based on reporting by The Associated Press. AP writers Darlene Superville and Suzanne Gamboa contributed to this report.