Former President George W. Bush, who failed to pass a comprehensive immigration bill when he was in office, on Wednesday said that he hoped there would be a "positive resolution" to Congress's immigration debate.
Speaking in Dallas at a naturalization ceremony hosted by The Bush Center, the two-term Republican president did not endorse any specific bill, but said, "We have a problem. The laws governing the immigration system aren't working ... the system is broken."
The call for comprehensive reform resonates with some Republican senators, who have to run in statewide elections, and with some prospective Republican presidential candidates.
But it is much less of an incentive for House Republicans, many of whom fear conservative Tea Party challenges if they back a pathway to citizenship for the 11 million, a core demand of Obama and his fellow Democrats.
According to a recent study by the nonpartisan Cook Political Report, which tracks congressional races, only 24 of the 234 House Republicans represent districts that are more than 25 percent Hispanic.
The study found that 148 of the Republican-held districts are less than 10 percent Hispanic, and another 62 are between 10 percent to 25 percent Hispanic.
David Wasserman, who conducted the Cook study, said most House Republicans believe they could defeat a Democratic challenger in the general election.
"But they don't know if they will face a Republican primary challenge if they vote for an immigration bill backed by the president," Wasserman said.
Republican Representative Steve Scalise of Louisiana, who heads a large group of House conservatives, told reporters: "In the House, we plan on addressing border security front and center. It has got to be the main component of anything that is done on immigration."
The House Homeland Security Committee has approved a border security bill that could be considered as a stand-alone immigration measure on the House floor.
It would direct the Department of Homeland Security to develop and implement a plan to control the entire southwestern border within five years and be able to catch or turn back 90 percent of illegal entries.
Meanwhile, the House Judiciary Committee has produced four targeted bills, which also could see action in the House. They include a tough measure aimed at finding and punishing those living in the United States illegally and another to help U.S. high-tech firms hire more skilled labor from abroad.