Republicans are warming to the idea of reforming the "broken" U.S. immigration system in the wake of their defeat in this week's presidential election by Democratic incumbent Barack Obama, who was the choice of 70 percent of Hispanic voters.

Among those raising the issue after Tuesday's loss at the polls is the GOP's highest-ranking elected official, House Speaker John Boehner, who speaks of the need for a plan to deal with the estimated 11 million undocumented immigrants now in the country.

"What I'm talking about is a common-sense, step-by-step approach to secure our borders, allow us to enforce the laws and fix a broken immigration system," he said Friday at a press conference.

"It's just time to get the job done," Boehner said, though declining to offer any specific ideas.

Expressing Republicans' willingness to work with Democrats, the speaker stressed that "on an issue this big, the president has to lead."

Latinos voted even more overwhelmingly for Obama on Tuesday than they did four years ago, thanks perhaps to Republican candidate Mitt Romney's comments about "self-deportation" as a solution to unauthorized immigration.

Even before Boehner spoke out, one of the Republicans' rising stars, Florida Sen. Marco Rubio, urged his GOP colleagues to focus on immigrant communities.

The Cuban-born senator is already being touted as a possible presidential hopeful in 2016.

One alarming sign for the GOP is that 48 percent of Florida's traditionally staunchly Republican Cuban-American voters cast ballots for Obama, according to a poll by Bendixen & Amandi Internacional.

Another of the Republican Party's most prominent minority figures, former Secretary of State Condoleezza Rice, pointed out that the GOP is losing "important segments of the electorate."

"The changing demographics in the country really necessitates an even bigger tent for the Republican Party," Rice said on CBS' "This Morning" program. EFE