Latino influence is only expected to rise, as the number of Latinos who are eligible to vote is expected to nearly double over the next two decades. According to the Pew Hispanic Center, Latinos are expected to account for 40 percent of the electorate growth and they could total 40 million eligible voters by 2030, up from 23.7 million now.

But it wasn’t just Latinos who were seeking a more sympathetic policy for the undocumented community. Two-thirds of voters said undocumented immigrants working in the United States should be offered a chance to apply for legal status, according to exit polls. Only about one in three said they should be deported.

Obama said this week that an immigration plan must include the DREAM Act, which would give a path to citizenship to about 1.2 million young undocumented immigrants who were brought here by their parents.

But in his news conference this week, the president noticeably left out citizenship for the parents and other illegal immigrants in his broader call, saying only “path to legal status.”

Many Republicans oppose a path to citizenship, likening it to amnesty.

Republicans will have to compromise on providing a legal path for some illegal immigrants, but Graham said labor unions closely aligned with Democrats also would have to compromise on expanding guest-worker programs, which require participants to return to their home countries after specific periods. Some Democrats charge that the programs are schemes to import cheap labor to displace American workers.

Despite the warm feelings being expressed between Democrats and Republicans, immigration remains one of the more emotional divisive issues of our day. Obama has pledged to confront the issue soon after his inauguration Jan. 21.

While both sides agree that immigration needs to be addressed next year, they’re moving cautiously, as the last several attempts at comprehensive restructuring have failed. It’s been more than 25 years since the last comprehensive overhaul.

For many Republicans, the newfound advocacy comes with risks. Many voters continue to strongly oppose anything that smacks of “amnesty.”

Graham, who’s running for re-election in 2014, backed away from his earlier levels of support after an onslaught of criticism. McCain also is returning to negotiations after abandoning earlier support. Facing a conservative challenger in 2010, he released a tough-talking television ad that blamed illegal immigrants for “home invasions, murders” and called for completing the “danged fence.”

To reach any agreement, conservatives will have to be part of the discussions, Paul said. He’s willing to serve as a liaison.

A darling of the tea party movement, Paul once made headlines by saying he favored denying citizenship to the U.S.-born children of illegal immigrants. He now wants to set up roundtable meetings with Latino leaders to talk “trade-offs,” and he said this week that he supports an “eventual path” to citizenship.

Republicans are seeking to avoid the mistakes of 1986, when President Ronald Reagan granted amnesty to some 3 million illegal immigrants. A lack of security mechanisms contributed to a wave of millions more illegal immigrants coming to the country to be with family.

There’s a “consensus” among House Republicans to work toward a solution, said Rep. Peter King, R-N.Y., who serves as the chairman of the House Committee on Homeland Security. To get his support, he said, it’s crucial to “have enforcement mechanisms in there that are real.”