CNN  — 

Illegal immigration was not the debate that 2016 Republicans wanted to have right now as they begin an already tough battle to regain the White House.

Perhaps no issue has bedeviled Republicans in recent election cycles more than illegal immigration. GOP candidates have been snared, over and over again, by the difficulty of appealing to conservative GOP primary voters who dominate the primary process while not alienating Latino voters, whose influence has grown in battleground states with each presidential cycle.

This week, as the controversy raged on about the anti-immigrant comments of Donald Trump, his fellow GOP contenders found themselves seared by the damage that he was inflicting on the Republican brand. When Trump first made the inflammatory assertion in his June announcement speech that some illegal immigrants from Mexico are criminals and “rapists,” many of his rivals were slow to respond. But as the fallout has continued, more are speaking out – trying to reinforce that Trump’s views are not representative of the image of the Republican Party.

READ: Donald Trump digs in on immigration

Some, like Jeb Bush, have sharply criticized Trump’s remarks, while others like Marco Rubio – who has taken flak from conservatives for helping usher an immigration reform bill through the Senate – have seemed unwilling to engage beyond paper statements. And all of them will be tested on the issue before a national audience during the upcoming debates that will weed out the weaker contenders from the field.

By infuriating many Latino voters, who have pointed to a number of studies showing that crime is actually lower among illegal immigrants than the broader population, the debate has brought unwelcome comparisons to recent struggles by Republicans to talk about immigration in a way that broadens their appeal among minority voters.

It revived talk, for example, of Mitt Romney’s suggestion during the 2012 Republican primary that he was in favor of “self-deportation” for millions of illegal immigrants – a statement that made it extremely difficult for him to draw large numbers of Latinos to support his campaign when it mattered later in the general election.

RELATED: GOPers run from Trump on immigration stance

Clinton Jeb Trump UPDATE
Hillary Clinton on immigration and the GOP race
02:09 - Source: CNN

President George W. Bush’s strong performance among Latino voters – he notched 44% of the Latino vote in 2004 compared to Romney’s 27% in 2012, according to national exit polls – seems like a distant memory to many Republicans now, despite a focus on building goodwill among minority voters by Republican National Committee operatives.

“We’ve gone from 44% to 27% among Hispanic voters, for a reason. You’ll never convince me that it hasn’t been about the way that we’ve handled this issue,” South Carolina Republican Sen. Lindsey Graham said in a telephone interview with CNN on Tuesday.

“Mitt Romney showed a lot of political courage by saying that (his comment about) ‘self-deportation’ was a mistake, and now here we have Donald Trump casting 11 million people in a very derogatory manner. That’s a problem,” said Graham, who is also seeking the GOP presidential nomination. “There are some within the 11 million that are bad people, but I cannot tell you how harmful it is to reinforce a narrative that Republicans basically have very little respect for people.”

The Latino vote was a key factor in President Obama’s two victories, but by 2014 Republicans seemed to be making some limited gains. A survey by the Pew Research Center shortly before the 2014 elections showed that registered Latino voters were less supportive of the Democratic Party then in recent years. In the October 2014 Pew survey, Democrats still held a commanding edge among Latinos, but 27% of Hispanic voters said they leaned toward the Republican Party, which was up from 22% in 2012.

READ: Trump calls out Rubio for being “weak” on immigration, praises Cruz

Many Republican strategists have watched with alarm as Trump has sucked up all the oxygen in the presidential race on the issue, essentially doubling down on his comments by the day – even as huge national corporations abandon their ties to his business organization.

The danger for other Republican candidates in being painted as anti-immigrant as a result of Trump’s comments was evident Tuesday in Iowa when Hillary Clinton argued that the GOP candidates all basically hold the same position on illegal immigration and vowed that she would lead the way forward on a path to citizenship.

All of the GOP candidates, she told CNN’s Brianna Keilar in her first national television interview this election season, are “in the same general area on immigration. They don’t want to provide a path to citizenship. They range across a spectrum of being either grudgingly welcome or hostile toward immigrants.” Graham took issue with her comments, noting that he has long supported a path to citizenship.

“I’m going to talk about comprehensive immigration reform,” Clinton said Tuesday. “I’m going to talk about all of the good, law-abiding, productive members of the immigrant community that I personally know, that I’ve met over the course of my life, that I would like to see have a path to citizenship.”

READ: Trump’s immigration comments hurting GOP, Romney says

A number of Republican strategists said Tuesday that the candidates have an opportunity to stand out in a crowded field by forcefully taking on Trump, and moving the debate toward the policy realm.

They noted for example that candidates should debate the effect of sanctuary cities like San Francisco and whether law enforcement is properly tracking illegal immigrants with prior felony convictions in the U.S., like the undocumented immigrant accused of shooting San Francisco woman Kate Steinle on San Francisco’s Pier 14 last week.

“This is a discussion that we know is going to happen at some point anyway,” said Lanhee J. Chen, Romney’s former policy director and a fellow at Stanford University’s Hoover Institution. “Whether they engage in it sooner or later – I think for the 2016 candidates what they ought to be thinking about, quite frankly, is what they are going to say substantively and what their policies are going to be.”

“The Trump stuff is silly and it’s just Trump being Trump,” Chen said. “But if they are able to engage on the substance, it could be good for the Republican Party, particularly if the place where we end up is perceived as being more reasonable than in the past.”

The debate over whether city and federal officials could have done more to prevent Steinle’s murder in San Francisco is likely to keep the illegal immigration issue at the forefront in the coming weeks – and it is likely to come up when the presidential debates begin in August.

Trump has seized on the circumstance surrounding Steinle’s murder as justification for his comments that some Mexican immigrants are criminals and rapists. The suspect in Steinle’s death, undocumented immigrant Juan Francisco Lopez-Sanchez, has a felony record and was deported to Mexico five times.

Trump: San Francisco killing shows perils of illegal immigration

Keying off that point, Trump released a new statement on Monday: “What can be simpler or more accurately stated? The Mexican Government is forcing their most unwanted people into the United States. They are, in many cases, criminals, drug dealers, rapists, etc.,” he said. “This was evident just this week when, as an example, a young woman in San Francisco was viciously killed by a five time deported Mexican with a long criminal record, who was forced back into the United States because they didn’t want him in Mexico.”

Trump argued that the Steinle case was “merely one of thousands of similar incidents throughout the United States.”

Hillary Clinton weighed in on the matter during her interview with CNN on Tuesday.

Clinton, who attended Trump’s 2005 wedding, said she was “disappointed” by the real estate magnate’s comments. She went on to say that that Steinle’s murder pointed to the problems with the current immigration system.

In March, Lopez-Sanchez was placed in the custody of San Francisco police, who wanted him on an outstanding drug warrant, after he completed a federal prison sentence. The U.S. Immigration and Custom Enforcement says it requested notification before Lopez-Sanchez was released.

Clinton told CNN’s Keilar on Tuesday that city officials should have listened to the guidance of the Department of Homeland security, “which as I understand it, urged them to deport this man again after he got out of prison another time.”

“Here’s a case where we’ve deported, we’ve deported, we’ve deported. He ends back up in our country and I think the city made a mistake,” Clinton said in the interview. “The city made a mistake, not to deport someone that the federal government strongly felt should be deported. So I have absolutely no support for a city that ignores the strong evidence that should be acted on.”