Many House Republicans are chilly or openly hostile to the bipartisan bill before the Senate, embraced by President Barack Obama. Even substantial changes to the bill may do little to placate these lawmakers, who demand strict crackdowns on unlawful border crossings and no "amnesty" for people here illegally.
These Republicans don't deny that weak support from Hispanic voters is hurting GOP presidential nominees. And they concede the problem may worsen if Latinos think Republicans are blocking "immigration reform."
These House members, however, worry much more about their own constituents' opposition to the proposed changes. And they fear a challenge in the next Republican primary if they ignore those concerns.
"It's hard to argue with the polling they've been getting from the national level," said Rep. Kenny Marchant, R-Texas, referring to signs of serious problems for Republican presidential candidates if immigration laws aren't rewritten. "I just don't experience it locally."
The proposed immigration overhaul "is very unpopular in my district," said Marchant, who represents suburbs west of Dallas. "The Republican primary voters, they're being pretty vocal with me on this subject." Besides, he said, "if you give the legal right to vote to 10 Hispanics in my district, seven to eight of them are going to vote Democrat."
Many colleagues concur.
"My district is not in favor of creating a system where people who committed a crime can jump in front of those who have tried to come here based on the law," said Rep. Walter Jones, R-N.C., describing what he fears the Senate will pass.
The Senate bill provides a pathway to citizenship for millions of people here illegally, but it tries to keep them from gaining citizenship ahead of people who went the official route.
Rep. Charles Boustany, R-La., summed up the dilemma for Republicans who care chiefly about electing presidents.
"Every member in the House is looking at the immigration debate through a prism of what's of concern in their district," Boustany said.
A Republican Party post-mortem of Mitt Romney's November loss to Obama concluded: "we must embrace and champion comprehensive immigration reform," or "our party's appeal will continue to shrink."
Sen. Lindsey Graham, R-S.C., said on NBC's "Meet the Press" Sunday: "If we don't pass immigration reform, if we don't get it off the table in a reasonable, practical way, it doesn't matter who you run in 2016."
"We're in a demographic death-spiral as a party," Graham said.
House Republicans, however, spend far more time talking and worrying about their own election prospects, not the next presidential nominee's.
"It's a classic challenge when the best interests of the party are at odds with the best interests of the majority of the members individually," said Rep. Tom Cole, R-Okla. He is close to Speaker John Boehner and other Republican leaders who want a major immigration bill to pass.
"What it takes to get a deal with a Democratic Senate and a Democratic president makes it extraordinarily difficult for a lot of (House) members," Cole said, "because it can cause you a big problem in your primary."
Some lawmakers say Boehner might allow a far-reaching immigration bill to pass the House even if most Republicans oppose it, with Democrats providing most of the votes. Boehner has chosen that "minority of the majority" route on some less consequential issues. Republicans, however, say it would be harder politically to use the tactic on something as momentous as rewriting the nation's immigration laws.
Rep. Steve Chabot, R-Ohio, exemplifies the leadership's challenge.
"A lot of people do believe that the Republicans need to get this issue behind us for presidential politics purposes," Chabot said. But they "are willing to go a lot further in reaching some agreement than a lot of us believe is good for our country."
Chabot said he would not consider an immigration bill without "very substantial border control" and a visa policy that punishes those who "cut in front of the line by just coming here illegally." The current Senate bill fails those tests, he said.
Rep. Jason Chaffetz, R-Utah, said the Senate bill "is not palatable at this point" because it would allow "amnesty and lack of security" on the border.
Such opposition can't be pinned solely on the politics of isolated House districts. Republicans running statewide for the Georgia Senate seat, for instance, are among the immigration proposals' toughest critics.
"Everybody is committed to getting the issue dealt with," said Rep. Jack Kingston, but "the Senate amnesty bill probably is not going to do well in the House."
Rep. Paul Broun, also seeking Georgia's Senate nomination, said any immigration deal "must make English the official language of the country." The U.S.-Mexican border, he said, must be secured "totally, whatever it takes. A double fence high enough to make sure it's secure."
Some Republicans wince at talk of massive double fences and making English the official language. They say it fuels arguments that the GOP is unwelcoming to all Hispanics, legal or not.
The "amnesty" issue may be tougher legislatively. The Senate bipartisan team says its bill will collapse without a pathway to citizenship for millions of immigrants here illegally.
Supporters say the proposed pathway isn't "amnesty" because immigrants would have to earn citizenship through an arduous route that includes paying fines and taxes.
It's unclear how many House Republicans will buy that argument.
Defining "border security" also is crucial. The Senate bill's goal is for 90 percent of would-be crossers to be caught or turned back. But it doesn't make citizenship contingent on that target.
Several House Republicans say a border enforcement level of at least 90 percent must be documented before any pathway to permanent legal status—whether citizenship or not—could be started for the millions here illegally.
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