While some Republican senators have introduced legislation they say signals the party's move toward immigration reform, some immigrant advocacy groups have criticized those efforts.

"Republicans seem to realize that Latino voters have serious electoral clout, but so far, they've just been paying lip service to the issue," said Lorella Praeli, advocacy and policy director of United We Dream (UWD), which has been pushing for the passage of the DREAM Act. "We expect better than the cynical political proposals we've seen."

Measures like the ACHIEVE Act, introduced last week by Sen. Jon Kyl (R-AZ) and Sen. Kay Bailey Hutchison (R-TX) and also sponsored by Rep. John McCain (R-AZ), and the STEM Jobs Act, she said, fell short of the demands.

ACHIEVE is being promoted as the party's answer to both the DREAM Act, which failed in Congress following a partisan impasse two years ago, and the Deferred Action for Childhood Arrivals (DACA) initiative signed into effect by President Barack Obama this past summer.

However, ACHIEVE does not offer a path to full citizenship, one reason why the Congressional Hispanic Caucus has already rejected it, with Rep. Luis Gutierrez (D-IL) calling it "too little too late."

Arturo Carmona, executive director of Presente.org, told The Raw Story ACHIEVE fell short the legal and personal needs that immigration reform should achieve.

"The Republican party continues to listen to its right wing, that's said that [it will support] no new net-positive immigration agreements," Carmona said.

Both Carmona and Praeli said their groups are planning how to continue their respective campaigns after Obama's second inauguration next month; Praeli mentioned UWD is looking to meet with not only Gutierrez, but House Speaker John Boehner (R-OH) and other GOP lawmakers, armed with a new platform calling for citizenship as a destination point for the country's 11 million undocumented immigrants, as well as the elimination of programs like Secure Communities and E-verify, which it feels targets their members' communities.

"The zero-sum game is just that - a game," Carmona said. "It's not gonna move the debate forward."