John McCain
John McCain is a U.S. senator from Arizona. Reuters

Sen. John McCain added his voice on Sunday to a growing chorus of Republicans calling for immigration reform, underscoring the issue’s emergence after an election in which Democrats resoundingly won the Latino vote.

America’s Hispanic population has surged over the past decade, and McCain alluded to how the country’s shifting demographics are altering the political landscape. In an appearance on "Fox News Sunday," the Arizona Republican said his party would need to adapt.

“We have to have a bigger tent. No doubt about it. And obviously we have to do immigration reform,” McCain said. “There is no doubt whatsoever that the demographics are not on our side.”

McCain is not the first Republican to stress this point. Former Florida Gov. Jeb Bush has become the party’s leading spokesman for a more welcoming immigration stance, warning that the strident pro-enforcement rhetoric pervading much of the debate cannot compete with the growing clout of Latino voters.

The Sunday after President Barack Obama won a second term, Sen. Lindsay Graham, R-S.C., appeared on “Face the Nation” and acknowledged that a hardline stance on immigration had "built a wall between the Republican Party and the Hispanic community."

"This is an odd formula for a party to adopt -- the fastest-growing demographic in the country -- and we're losing votes every election cycle. And it has to stop. It's one thing to shoot yourself in the foot. Just don't reload the gun,” Graham said, adding that “I intend to tear this wall down and pass an immigration reform bill that's an American solution to an American problem.”

Sen. Charles Schumer, D-N.Y., has said he and Graham are at work on drafting immigration legislation that would strengthen border security and background checks intended to prevent undocumented immigrants from finding work. The plan would also establish a temporary worker program and create a path for undocumented immigrants in the U.S. to obtain legal status.

House Republicans, meanwhile, are reportedly planning a vote on legislation that would provide more visas to foreign students who study science and technology in the United States. There is broad bipartisan support for measures that would make it easier for foreigners studying so-called STEM (Science, Technology, Engineering and Mathematics) topics to remain in the country -- both Obama and Republican presidential nominee Mitt Romney endorsed it -- but the issue has become entangled in other thorny immigration questions.

When a STEM bill came up for a vote last year, House Democrats blocked it because the legislation would have offset the increase in STEM visas by scaling back other categories. The new bill sweetens the pot by making it easier for the spouses and children of green card holders to settle in the United States while they wait for their own green cards.

Obama did not get any significant immigration measure through Congress during his first term, angering immigration advocates who said he had reneged on his promise to pursue comprehensive reform while presiding over record numbers of deportations. The DREAM Act, a bill that would have opened a path to citizenship for undocumented immigrants who were brought to the United States as children, died in the Senate in 2010.

But things could be different this time. Obama has repeatedly said Republican intransigence is preventing negotiations on a comprehensive immigration reform bill. Before the election, Obama predicted that, should he win a second term, Republicans would have an incentive to come to the table and would have “a deep interest in getting [immigration reform] done.”

The president reiterated that point in a Nov. 14 news conference, saying he expected to “begin the process in Congress, very soon after my inauguration.”