WASHINGTON (AP) — A Congress that began with bright hopes for immigration legislation is ending in bitter divisions on the issue even as some Republicans warn that the political imperative for acting is stronger than ever for the GOP.

In place of a legislative solution, President Barack Obama’s recent executive action to curb deportations for millions here illegally stands as the only federal response to what all lawmakers agree is a dysfunctional immigration system. Many Democrats are convinced Latino voters will reward them for Obama’s move in the 2016 presidential and Senate elections, while some Republicans fear they will have a price to pay.

“If we don’t make some down payment toward a rational solution on immigration in 2015, early 2016, good luck winning the White House,” said Republican Sen. Lindsey Graham of South Carolina, an author of the comprehensive immigration bill that passed the Senate last year with bipartisan support, but stalled in the GOP-led House.

With the expiration of the 113th Congress this month, that bill will officially die, along with its path to citizenship for the 11 million immigrants in this country illegally.

Immigration is certain to be a focus for the new, fully Republican-led Congress when it convenes in January — but there’s little expectation the GOP will make another attempt at comprehensive reforms.

Instead, GOP leaders in the House and Senate have pledged to take action to block Obama’s executive moves, setting up a battle for late February when funding expires for the Department of Homeland Security, which oversees immigration matters. House Speaker John Boehner, R-Ohio, has promised action on a border security bill as part of that.

Whether Congress can do anything to stop Obama remains unclear, since he’s certain to veto any effort to undo his executive moves. It’s also not clear lawmakers could pass a border bill, or that Obama would sign it if they did.

While some congressional Republicans are arguing for action on piecemeal reforms, most advocates are resigned to waiting until a new president takes office in 2017 for lawmakers to make another attempt at a comprehensive overhaul that resolves the central immigration dilemma — the status of the millions here illegally.

“They had the best chance in a generation and they couldn’t get enough support from the Republican caucus,” said Frank Sharry, executive director of America’s Voice, an immigrant advocacy group. “It may well be that they’re going to have to lose the White House and both chambers of Congress for us to get comprehensive immigration reform.”

When Obama won a second term in 2012 with strong Hispanic and Asian support, many national Republican leaders decided they needed to support policies that would attract those growing blocs of voters. The Republican National Committee formally embraced support for comprehensive immigration reform as a guiding principle for the GOP.

But legislative efforts stalled in the House as conservative Republicans balked at Boehner’s efforts to advance the issue. Last summer’s crisis over an influx of unaccompanied Central American minors arriving at the border caused shelter overloads and case backlogs, straining resources and creating the impression that the border was out of control — further souring political prospects for reform legislation.

In absence of congressional efforts, Obama promised he would act on his own, and he made good on that shortly after last month’s midterm elections, announcing an array of changes that will include work permits and three-year deportation stays for some 4 million immigrants here illegally. It mostly applies to those who’ve been here more than five years and have kids who are U.S. citizens or legal permanent residents.

The move inflamed Republicans, who have been fighting about it ever since, including a failed effort by Sen. Ted Cruz, R-Texas, to block Obama in a Senate floor vote this past weekend. On Tuesday the dispute spilled over into debate on Obama’s nominee to lead the Immigration and Customs Enforcement agency, Sarah Saldana, the U.S. attorney in Dallas. She was confirmed 55-39 by the Senate over objections from Republicans who had initially supported her but turned against her because of her support for Obama’s executive actions.

Meanwhile, some immigration advocates complained that the steps didn’t go far enough as Obama faced criticism from both sides of the political divide.

A new Associated Press-GfK poll found that most Americans support allowing immigrants living in the country illegally a way to stay here lawfully. But only 43 percent of them think Obama was right to take executive action to make those changes, while 54 percent of them say he should have kept trying to make a deal with Republicans. Still, the poll also showed little sign of blowback for Obama. Although 57 percent disapprove of Obama’s handling of the immigration issue, that was down slightly from 63 percent in October.

A group of 24 states joined in a federal lawsuit filed in Texas alleging that Obama overstepped his constitutional powers in a way that will only worsen the humanitarian problems along the southern U.S. border. And Arizona Sheriff Joe Arpaio is in federal court in Washington, contending that the policy is a magnet for more illegal entries into the country that will impose a burden on law enforcement.

In a court filing late Monday, the Justice Department argued for dismissal of Arpaio’s case, saying he has failed to substantiate his claims.

Congressional Republicans say that Obama’s actions created an even tougher climate for immigration legislation, but many Democrats and advocates contend that Republicans were terminally stalled on the issue anyway. Some Republicans question whether immigration legislation really is a political imperative for the GOP. “It’s really mixed out there — some people want a big immigration bill, others don’t,” said Sen. Orrin Hatch, R-Utah, a supporter of reform efforts.

And two years after a “Gang of Eight” senators launched an immigration overhaul drive on Capitol Hill, some of those same players say they have no plans to initiate another such effort.

“I’m not going to start it in the Senate,” said Sen. John McCain, R-Ariz. “We’ve tried that.”

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Associated Press News Survey Specialist Emily Swanson and writer Pete Yost contributed to this report.

• Politics & Government
• Immigration Issues
• Barack Obama