The national Republican Party leadership has studied the results of the 2012 election, and one of the conclusions they came to was that the party needed to reach out to the minority community or they would have trouble winning future elections. This is because the white portion of the electorate is diminishing with each election, and the Republicans are currently doing very poorly with minority groups (having lost more than 70% of the votes of all minority groups in 2012).
One of the things the national party suggested was that Republicans in Congress should support an immigration reform bill -- a bill that would not only strengthen border controls, but also provide a path to citizenship for undocumented people living in this country. This would not only put them in line with the wishes of about 60% of Americans, but they hope it would play well in the Hispanic community (where immigration reform is considered a very important issue).
It's a good idea, and a few Republicans in Congress are seemingly willing to go along with the national party's wishes. But others are reluctant to climb on board with immigration reform. Some are tea baggers, and hold ideology to be more important than growing the party and winning national elections. The rest find themselves between a rock and a hard place. They would like to reach out to Hispanics, but they know that will only anger the party's base. This is why candidates considering a run for national office, like Marco Rubio and Jeb Bush, have recently backed off supporting immigration reform -- since it could kill their chance of getting the party's presidential nomination.
And their fears are well-founded. The Republican base is far more anti-immigrant than the party leadership, and are not yet willing to give up their anti-immigrant bigotry. This was recently illustrated in a Washington Post/ABC News Poll -- taken between March 27th and 30th of a national sample of 1,016 adults (with a margin of error of 3.5 points).
While the poll shows that 57% of the general public supports an immigration bill with a path to citizenship (including 73% of Democrats and 58% of Independents), it is very different among the GOP's base voters. Only 35% of Republicans support a path to citizenship, while 60% oppose it (and 2/3 of those oppose it very strongly). These voters simply haven't (at least yet) bought into the need for immigration reform or the need to reach out to Hispanics (the fastest growing minority group in the United States).
It will be interesting to see what the congressional Republicans do in the next few months. Will they reach out to Hispanics by supporting immigration reform, and anger a significant majority of their base? Or will they kill immigration reform, and throw away their chance for the presidency in 2016 (and maybe even hurt themselves in the 2014 elections)? It's a real dilemma for them.