If there was any doubt about how determined Republicans are to make inroads with Hispanic voters, just look at the reaction to Rep. Steve King's claim that many undocumented high school graduates are "hauling ... marijuana across the desert.”

The Iowa Republican's comments, made in a Newsmax interview last week, surfaced Tuesday on liberal blogs. Rather than dismiss the controversy as a distraction, House GOP leaders have come out in force to condemn their colleague. House Speaker John Boehner (R-Ohio) called them “wrong” and “hateful,” House Majority Leader Eric Cantor (R-Va.) “inexcusable.”

On Thursday Boehner went further, telling reporters that King's words were "hateful and ignorant." He added, "What he said does not reflect the values of the American people or the Republican party."

King is undeterred. “When people start calling you names, that’s what confirms you've won the debate," he said Wednesday. His goal: to derail a Republican version of the DREAM Act, which would legalize illegal immigrants who came to the U.S. as children and graduated high school.

So King won't back down, and his intransigence shows how treacherous immigration reform is for Republicans. The closer the party moves to passing real reform and beginning to repair its relationship with the Latino community, the angrier opponents within the GOP will get -- and the more likely they are to make comments that can be used in Democratic attacks.

Boehner himself acknowledged Thursday that comments like King's "make it more difficult" to pass immigration legislation, "but I'm going to continue to work with members who want to get to a solution as opposed to doing nothing at all.”

There's particular danger in a drawn-out debate over immigration reform. The more methodical the House deliberations are, the more opportunity for reform opponents to make incendiary comments. And until House Republicans come out with a bill (or series of bills) there will be nothing but words to define the GOP effort.

Comments like King's are especially damaging if reform fails, and Republicans are left to make the case that they tried to pass it in good faith. A major hurdle Republicans face with Hispanic voters is the empathy gap. By a 50-point margin, Latino voters say the Democratic Party has more concern than the Republican Party for Latinos.

Republicans in Latino-heavy districts are already feeling the heat, as seen by this tweet from Rep. Jeff Denham (R-Calif.):

It's hard for most Republicans to completely distance themselves from King because there's agreement with some of his concerns -- though not his rhetoric. A King-sponsored measure to defund an executive order styled after the DREAM Act passed the House last month with only six Republican "nay" votes. (Denham was one of them).

There's been some talk among anti-reform conservatives that the GOP cannot and should not attempt to win over Latinos, who, the argument goes, are inclined towards the Democratic Party regardless.

For some, King and the reaction to him are just more evidence that granting illegal immigrants a path to citizenship is no panacea for the party.

"If amnesty passed today, Steve King would still very much be around tomorrow," the Washington Examiner's Conn Carroll wrote.

King himself would want GOP leaders to reach the same conclusion, but a majority of House Republicans want to work on the issue, even if they don't agree on how. He can't change that. But he can make the process as painful as possible.