Comprehensive immigration reform faces tough opposition in the conservative House of Representatives, but there are signs that Republicans may be changing their minds.

The Senate's bipartisan "Gang of Eight" has begun a targeted campaign aimed at convincing influential House Republicans to support immigration reform and a path to citizenship for many of the 11 million undocumented immigrants currently living in the country.

Support among conservatives, even those vocally opposed to immigration reform, is likely higher than it seems. While privately many Republicans are aware that killing the reform bill would doom their party's chances with Hispanics for years to come, publicly they must denounce reform efforts to avoid primary challenges next year from even more conservative candidates.

That leaves the Republican leadership in an odd position. House Speaker John Boehner has already declared he will not bring the reform bill to a vote on the House floor unless it has the support of a majority of Republicans. But with many of those same Republicans refusing to admit they support the bill, that may never happen, unless senators can convince Boehner to present the bill anyway.

Some Republicans, like Raul Labrador of Idaho, have suggested a piecemeal approach to reform that wouldn't grant citizenship to any undocumented immigrants, but President Obama again reiterated that is not an option during an interview with Telemundo on Tuesday.

Now one of the most prominent anti-immigration reform voices, Gary Miller of California, has backtracked on some of his previous language, removing references to "amnesty" and "anchor babies" from his website, terms considered misrepresentative or offensive by immigration reform proponents.

That Miller was recently redistricted and now faces an election with half of his new constituency composed of Latinos could have something to do with his new outlook. But most other Republican representatives are in comfortably red districts, leaving them with little incentive to reexamine their position. It could be up to Boehner to crack the whip, lest he relegate the Republicans to a unicameral party for the foreseeable future.