WASHINGTON - Congressional Republicans are pronouncing President Obama's proposal that the next Congress overhaul the country's immigration laws as dead before arrival.

In his year-end news conference Wednesday, Obama said his biggest regret about the recent lame-duck session of Congress was the defeat of the Dream Act, a measure that offered a path to citizenship for undocumented immigrants brought to the country as children.

"It is heartbreaking," Obama said, as he explained how such immigrants often realized that they were without legal status only when they tried to go to college or join the military. "That can't be who we are. To have our kids, classmates of our children, who are suddenly under this shadow of fear through no fault of their own. They didn't break the law - they were kids."

Congressional Republicans said in interviews Thursday that their concerns about the measure remained strong, and both House and Senate GOP leaders said they would fight any attempt to legalize any of the 11 million undocumented immigrants in the country before the administration secured the nation's southern border with Mexico.

"It is pointless to talk about any new immigration bills that grant amnesty until we secure the border, since such bills will only encourage more illegal immigration," incoming House Judiciary Chairman Lamar Smith, R-Texas, said in a prepared statement.

In an interview, Rep. Steve King, R-Iowa, ranking Republican on the House immigration subcommittee, accused Obama of playing politics with immigration and toying with Latino voters.

"It is extraordinarily unlikely that any version of comprehensive immigration reform that includes amnesty will go through the House of Representatives," he said.

Obama's call on Congress to pass the Dream Act "polarizes Americans along the lines of race and ethnicity," King added. "He implies there is a realistic chance - he knows better, and therefore it makes it a political statement designed to gin up his base and pit Americans against Americans."

During the recent contentious congressional debate over the act, Republicans said the measure would reward violators of the country's immigration laws and encourage new waves of illegal immigration. They also said that the measure was lax in allowing some lawbreakers to gain citizenship, and that the requirement that Dream Act beneficiaries obtain two years of college education or military service set the bar too low.

Revising the act to eliminate those issues would not solve the underlying problem with the measure, said Stephen Miller, a spokesman for Sen. Jeff Sessions, R-Ala., who led Senate Republicans in their opposition to the measure.

"When you're traveling in the wrong direction, modest alterations don't make a difference," Miller said. "You need to get off the road and head down a different one. As Senator Sessions has said, the first thing we need to do is end the massive illegality at the border."

Obama said Wednesday he is open to new measures to improve border security.

"I think it is absolutely appropriate for the American people to expect that we do not have porous borders and anyone can come in here any time," he said. "But I also think about those kids, and I want to do right by them."