A divisive congressional debate on immigration in 2006 and 2007 "built a wall" between Republicans and Hispanic voters, Graham said on CBS' "Face the Nation" program. "I intend to tear this wall down and pass an immigration reform bill that's an American solution to an American problem," he said.
Schumer said on NBC's "Meet the Press" that he's discussing the overhaul legislation with Graham. Republican interest in the issue is elevated after President Barack Obama captured 71 percent of the nation's fast-growing Hispanic vote in his re-election last week.
"The Republican party has learned that being anti-illegal, anti-immigrant, doesn't work for them," Schumer said.
The Census Bureau estimates there were about 10.8 million unauthorized immigrants living in the U.S. in 2010, more than half of them Mexican. Obama's re-election opponent, former Massachusetts Governor Mitt Romney, advocated a program he called "self-deportation" for illegal immigrants that would require them to leave the country to receive legal status. Democrats say such a plan is unworkable; Graham agreed.
"This issue has been around far too long," Boehner said in an interview with ABC News. "A comprehensive approach is long overdue, and I'm confident that the president, myself, others can find the common ground to take care of this issue once and for all." Graham said an overhaul would start by securing U.S. borders and making it more difficult for U.S. firms to hire illegal immigrants. The legislation would create a "guestworker" system for immigrants, he said, and require illegal immigrants to pay taxes and fines to gain legal status. Those seeking citizenship would have to learn English and "get in back of the line," he said.
"It could take over a decade to get a green card," he said.