For two decades, immigration has largely split the Republican Party into two camps. The first wants to make a number of changes in the nation's border and immigration programs, including finding a path for some of the 11 million people living in the country illegally to be become citizens. The second wants to focus primarily on border security.
Attempts to bridge that gap are tricky, as demonstrated by this week's surprise primary defeat of House Majority Leader Eric Cantor.
Where some of the party's top presidential prospects stand on the issue:
Sen. Rand Paul of Kentucky
Paul in 2013 proposed reinforcing border control efforts while allowing working immigrants living in the U.S. illegally to stay in the country and eventually obtain citizenship but not ahead of those here legally. The ideas received a tepid response when Paul spoke a year ago at the Iowa GOP's spring fundraising dinner.
After Cantor's defeat, Paul carefully restated his support for allowing workers to stay if they seek special visas, and he discussed what he called the "problem" of mass deportation.
"If you are not deporting people, does that mean you are normalizing them, and is that amnesty?" Paul said. "And so I really think that some of it, we're trapped in this rhetoric and we have to get beyond that."
Gov. Scott Walker of Wisconsin
As a candidate in 2010, Walker said he would sign a law like one in Arizona that allows local police to stop people suspected of living in the country illegally. He also called for barring immigrants here illegally from state health care and college benefits.
Last year, he told an editorial board meeting he'd support a path to citizenship for immigrants under some circumstances. On Thursday, though, he said in an interview with The Associated Press that his comments had been misconstrued. "I've never supported any firm amnesty," Walker said.
Gov. Chris Christie of New Jersey
Christie signed a version of the DREAM Act to allow children in New Jersey of parents who are living in the country illegally to pay in-state college tuition.
"I shouldn't have to make that decision," Christie said in February, describing the move as in New Jersey's economic interest. "There should be a national policy on how we protect our borders, how we orderly permit folks to enter this country, the orderly process for legalization of those folks."
Christie hasn't said much about immigration since then. But his position, which includes supporting a process by which people in the country illegally may attain citizenship, puts him at odds with parts of the GOP base.
Sen. Ted Cruz of Texas
Cruz's position, a spokeswoman said Thursday, "remains the same — we need immigration reform that celebrates legal immigration, not amnesty."
Previously, Cruz has criticized the Senate immigration measure led by Sen. Marco Rubio and also has said that Congress shouldn't even tackle the issue until 2015, since the GOP is likely to retake the Senate in November.
"Republicans are poised for an historic election this fall — a conservative tidal wave much like 2010," Cruz said in January. "The biggest thing we could do to mess that up would be if the House passed an amnesty bill — or any bill perceived as an amnesty bill — that demoralized voters going into November."
Sen. Marco Rubio of Florida
Rubio played a key role in brokering a bipartisan Senate immigration deal that led to passage of a bill to tighten border security, revamp the nation's visa system and give most of the estimated 11 million immigrants here illegally an eventual path to citizenship.
But after a conservative backlash, the Florida Republican mostly dropped the issue, endorsing the House's piecemeal approach and warning Congress against an "all-or-nothing" strategy. On Wednesday, he reiterated that stance and said President Barack Obama has made it impossible for Republicans to work with him on the issue.
"There's legitimate concerns about rule of law," he said. "I think those have only been exacerbated by this administration's unwillingness to enforce the law."
Former Gov. Jeb Bush of Florida
For Bush, the debate over immigration is personal. His wife, Columba, grew up in Mexico. The two met while Bush was an exchange student there and she is now an American citizen. In a book last year, he suggested giving legal status, but not citizenship, to immigrants living in the U.S. illegally, which seemed to contradict his past statements on citizenship.
He has remained vocal on the issue and angered some conservatives in April when he called illegal immigration "an act of love" by people who want to provide for their families. On Thursday, a spokeswoman said Bush stood by his call for an overhaul of the nation's immigration system.
Former Sen Rick Santorum of Pennsylvania
Santorum has spoken of the GOP's need to help immigrants but stopped short of calling for legalization of those living in the country illegally. On Thursday, he released a statement calling Cantor's loss "a serious wake-up call to the GOP establishment."
"At the moment, Republican leaders in Washington are deeply out of touch with working Americans who see their jobs threatened by the federal government's refusal to secure our borders," he said.
Associated Press writers Nicholas Riccardi in Denver; Thomas Beaumont in Des Moines, Iowa; Philip Elliott in Washington; Scott Bauer in Madison, Wisconsin; Michael J. Mishak in Miami; Adam Beam in Frankfort, Kentucky; and Will Weissert in Austin, Texas, contributed to this report.