Immigration policy, a background issue for much of the presidential campaign, played a significant role in Tuesday night’s presidential debate, with both President Obama and Republican challenger Mitt Romney going on the offensive.

Romney repeatedly criticized Obama for not pushing harder to get a comprehensive immigration overhaul package through Congress, noting that for the first two years of the president’s administration, Democrats held majorities in both chambers. The topic has been a sore spot among the president’s backers who wanted to see legislative change to the system.

“When the president ran for office, he said that he’d put in place, in his first year, a piece of legislation . . . that would reform our immigration system, protect legal immigration, stop illegal immigration,” Romney said. “He didn’t do it.”

In a later exchange, Romney made a similar promise of his own. “I’ll get it done,” he said. “I’ll get it done. First year.”

Obama said that immigration had been turned into a “divisive political issue” and that while he could deliver Democratic votes, an overhaul lacks bipartisan support.

The president said he met with members of both parties when he took office, but he blamed Republicans for opposing a comprehensive immigration overhaul, including those in the Senate who previously supported it. He blamed Romney for setting that tone, at one point comparing him unfavorably to former President George W. Bush, who unsuccessfully pushed for an immigration overhaul. Romney denied the charge.

Obama embraced his record of administrative action, which has been the target of much GOP criticism. He touted an increased Border Patrol presence, lower rates of illegal crossing in the Southwest, and his administration’s decision to prioritize for deportation those illegal immigrants who have committed crimes or are dangerous, rather than those whose violations solely concern immigration law.

“We’re going to go after folks who are here illegally, we should do it smartly and go after folks who are criminals, gang bangers, people who are hurting the community, not after students, not after folks who are here just because they’re trying to figure out how to feed their families,” the president said.

The DREAMers

Although he did not mention it by name, Obama referenced his administration’s new “deferred action” program that offers certain young illegal immigrants brought to the United States by their families two-year reprieves from deportation if they are pursuing educational opportunities.

“We should make sure that we give them a pathway to citizenship,” Obama said. The deferred action program does not provide such a pathway, but the president has supported Democratic-backed legislation (HR 1842, S 952) known as the DREAM Act, which would create that pathway and on which the deferred action policy was modeled.

Romney also reached out to young illegal immigrants.

“The kids of those that came here illegally, those kids, I think, should have a pathway to become a permanent resident of the United States and military service, for instance, is one way they would have that kind of pathway to become a permanent resident,” he said.

Romney said that he will not grant “amnesty” to illegal immigrants living in the country, adding that there are millions waiting to use the legal immigration system, which he said he wants to streamline. The former governor also said that he agrees with Obama on prioritizing criminals and would not be in favor of “rounding up” other illegal immigrants in the country for removal. Instead, he referred to the concept of “self-deportation” he has articulated in his campaign.

“What I was saying is, we’re not going to round up 12 million people, undocumented illegals, and take them out of the nation,” he said. “Instead, let people make their own choice. And if they find that they can’t get the benefits here that they want and they can’t find the job they want, then they’ll make a decision to go a place where they have better opportunities.”

Obama attacked Romney’s record on those points, noting that the former governor said during the Republican primary season that he would veto the DREAM Act and had characterized self-deportation as “making life so miserable on folks that they’ll leave.”

Arizona Law

The two candidates also sparred over remarks Romney made during a February primary debate, when he called Arizona’s tough immigration enforcement law a “model” and said he would drop a Justice Department lawsuit against it — which the Supreme Court later largely ruled in favor of — on “day one.” Obama criticized the Arizona law, and Romney’s support of it.

“Part of the Arizona law said that law enforcement officers could stop folks because they suspected maybe they looked like they might be undocumented workers and check their papers,” the president said. “You know what? If my daughter or yours looks to somebody like they’re not a citizen, I don’t want to empower somebody like that.”

Romney, however, said he was speaking only about a portion of the Arizona law dealing with E-Verify, the federal online employment authorization checking system. “That was a model for the nation,” he said.

Obama retorted that Romney’s “top adviser on immigration is the guy who designed the Arizona law, the entirety of it — not E-Verify, the whole thing.” Kris Kobach, an influential Republican currently serving as Kansas secretary of state and an architect of tough enforcement laws in Arizona and Alabama, has served as an informal adviser to the Romney campaign.

A version of this story first appeared on CQ Homeland Security.