A big part of that equation has to do with increasing support among Latino voters. Not only did the overwhelming support of Hispanic voters help deliver Mr. Obama his re-election this year, but as the fastest-growing population in the U.S., Latinos will be an increasingly crucial voting bloc going forward. Romney is believed to have been badly damaged among Latinos by his harsh rhetoric on immigration reform during the primaries - one of his suggestions included "self-deportation" - as well as the party's generally unsympathetic tone on the subject.

In recent years, according to Ayres, Republicans "persuaded themselves that they could use very harsh language about undocumented Hispanics without offending those who are here legally, but that was very misguided." In his report, "The Hispanic Challenge and Opportunity for Republicans," he argues that fixing the nation's immigration system is just one of the many measures the party will have to adopt in order to make serious inroads into the community.

It's clear that lawmakers are getting the message: Many congressional Republicans have already softened their tone with regard to immigration, and Republican members of both the House and the Senate put forth immigration-related bills within just weeks of the election.

"A great many Republicans already have the right tone: People like Jeb Bush and Marco Rubio promote conservative policies of limited government in a way that is very welcoming to new people who might not have been Republicans in the past," Ayres said. "So it's not like we don't have examples out there."

Talk vs. action

Despite the recent display of inclusiveness, it's unclear how far the GOP is willing to go on a policy level to make way for new members, and some wonder how fast change can feasibly come to a party that's dominated by elderly white men.

Immigration reform activists point out that neither of the recent GOP immigration bills - the STEM Jobs Act in the House and the ACHIEVE Act in the Senate - included a path to citizenship, which many see as imperative for their support. Ayres argues that it would be difficult to get a comprehensive bill through Congress, and that Democrats, who seek an overhaul to the nation's immigration system, "are in real danger of making the perfect the enemy of the good." He says the Republican Party can improve its standing among Latinos even without a bill that includes a path to citizenship.

Many immigration activists, however, cite the path to citizenship as a legislative imperative, and dismiss the recent GOP efforts as meaningless posturing.

"I think it would be very difficult for the community to see a bill that does not include a path to citizenship as a fix to the broken immigration system. I don't see how they could possibly sell that and expect support from the community," Arturo Vargas, executive director of the nonpartisan NALEO Educational Fund, told CBS News. "It's absolutely critical that we find a way of making sure that these 11 million [undocumented] individuals are able to achieve some kind of normalcy in their lives - that they can work and become full participants in this society."