If Republicans didn’t know it before, they learned in the November elections how serious a problem they have in winning Latino voters. Republican presidential candidate Mitt Romney won only 27 percent of self-identified Latino voters, according to exit poll interviews.

Steve Pope / Getty Images Sen. Marco Rubio, R-Fla., speaks at a combination fundraiser and birthday party for Iowa Gov. Terry Branstad, on Nov. 17, 2012 in Altoona, Iowa.

As Republicans make their case to Latinos and with one prominent Latino Republican, Florida Sen. Marco Rubio, a possible contender for the 2016 presidential nomination, long-stalled measures to increase immigration and give legal status to people illegally in the United States will be on the congressional agenda in 2013.

On immigration, the lame-duck session of Congress is a time for political positioning and strategizing rather than legislating. Along with all his other strategic challenges, House Speaker John Boehner has to figure out just far he and a majority of his GOP members are willing to go on immigration and which of his members in the new Congress will need to be given a free pass on tough roll call votes so that they don’t get challenged by conservatives in Republican primaries in 2014.

Meanwhile this week Republican senators urged Senate Democratic leader Harry Reid to allow the Senate to vote on a bill passed by the House last week that would provide legal residency to more foreigners who have earned doctorates or master’s degrees in science, technology, engineering or math at U.S. universities. The House-passed bill, which won the support of 27 Democrats, would create new visa categories for 55,000 science, engineering and mathematics graduates of American universities and it would eliminate a visa lottery program designed to increase immigration from counties which traditionally haven’t been big sources of U.S. immigrants.

Sen., John Cornyn, R- Texas, told the Senate Wednesday that it makes no sense for the United States to not allow foreign scientists who get their Ph.D.’s at American universities to remain in this country to work. “We are cultivating human capital and then sending those individuals back home” to their countries of origin, when many of them would rather remain in America,” Cornyn said.

Rep. Luis Gutierrez, D-Ill., discusses the GOP's mean and sometimes nasty rhetoric towards Hispanics, how important immigration is to Latino voters, the meeting he's having with GOP lawmakers to discuss immigration reform and the need to do comprehensive reform now.

Romney made this same argument during his second debate with President Barack Obama, calling for giving legal permanent resident status “to people who graduate with skills that we need. People around the world with accredited degrees in science and math (ought to) get a green card stapled to their diploma, come to the U.S. of A. We should make sure our legal system works.”

But Clarissa Martinez de Castro, director of civic engagement and immigration at the National Council of La Raza, the nation’s largest Latino advocacy group, criticized the House bill as “trying to eviscerate one program to feed another – as opposed to trying to fix the entire system.”

The relative smallness of the number of visas in the House bill, 55,000, she said, “tells you right away that we’re just tinkering around the edges. What really is begging to be addressed here is making sure the system works.”

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She said the core of the immigration redesign next year will be “the legalization and path to citizenship for the people who are already in the country.” That makes sense, she said, because “you cannot build on a faulty foundation. And the reality is we have a number of people who have been in the country for a very long time. They are part of the workforce and it makes sense to figure out that piece and how the other pieces develop from that one.”

A leading Democrat on immigration policy, Sen. Charles Schumer of New York, told reporters at the Capitol Thursday, “The best way to go is a comprehensive package. What we’ve learned in the past is when you try to do it piecemeal, the pieces fall apart.”

Matt York / AP In this Nov. 6, 2012 file photo, Sen.-elect, current Rep. Jeff Flake, R-Ariz., waves during an election night party in Phoenix.

In the Senate next year, Republican senator-elect Jeff Flake of Arizona (one of the co-sponsors of immigration reform in 2006) and Sen. Mike Lee of Utah will likely be key GOP deal makers, as well as Sen. John McCain of Arizona and Sen. Lindsey Graham of South Carolina.

Ultimately members of Congress will need to grapple with a crucial policy question: what should be the balance between immigration based on family ties and immigration based on a person’s expertise, education, and training. Should the United States bring in more people with doctorates in biochemistry, for example, and fewer who happen to have a brother or other relative in the United States?

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What Romney tried to do during the campaign was to convey the idea that he was open to immigration but that it had to be done through legal means. Rubio repeated this theme Wednesday in remarks at a POLITICO breakfast. His party, Rubio said, had “allowed itself to be positioned as the anti-illegal (immigrant) party…. What we really need to be is the pro-legal (immigrant) party.”

At the center of Democratic initiatives on immigration for several years has been the DREAM Act, a bill offered by Sen. Dick Durbin, D- Ill., and others to allow illegal immigrants brought to the United States by their parents before age 16 to stay legally in the country. Durbin’s bill would require these people to earn a high school diploma, submit biometric data and undergo a law enforcement background check. His bill would allow such people to eventually apply for permanent legal residence and, after an additional three years, apply for citizenship.

When the Senate voted on the DREAM Act at the end of 2010, three Democrats who are all up for re-election in 2014, Sens. Max Baucus of Montana, Kay Hagan of North Carolina, and Mark Pryor of Arkansas, all voted against ending debate, supporting Republican efforts to kill the bill by means of filibuster. Two other Democrats, Sen. Jon Tester of Montana and Sen. Ben Nelson of Nebraska, also voted against cloture and the effort fell five votes short. (Nelson is retiring at the end of this year.)

The political calculus next year might be different if the DREAM Act provisions are embedded within a larger bill, perhaps one with incentives that could appeal to senators from conservative states such as Arkansas and Montana. In the immigration vote tally, both sides of the equation – Democrats and Republican – will be important.