President Obama and congressional leaders of both parties broke bread Friday at the White House for a post-election discussion on the issues of the day, including areas of possible compromise – and some longstanding areas of disagreement.

The lunch came three days after a sweeping Republican victory in Tuesday’s midterm elections, in which the GOP won control of the Senate. In opening remarks, Mr. Obama congratulated the Republicans for running a strong campaign, and then noted the frustrations of Americans over Washington’s inability to solve problems.

“I think they’re frustrated by the gridlock,” the president said at the table in the Old Family Dining Room. “They’d like to see more cooperation. And I think all of us have the responsibility, me in particular, to try to make that happen.”

Topics on the table included jobs, education, Ebola, and the Islamic State.

Then there’s immigration – the issue that threatens to blow up Obama’s relationship with the GOP leadership, even before the new Congress is seated in January. At issue is Obama’s pledge to take executive action on immigration before the end of the year, likely granting relief from deportation to several million people in the United States illegally. Critics call such a move “executive amnesty.”

The White House press office's readout on the lunch contained one line about immigration, separate from the discussion of areas of common ground.

“The president reiterated his commitment to taking action on immigration reform in light of the House’s inability to pass a comprehensive bill,” the statement said.

The office of House Speaker John Boehner (R), in its own readout of the meeting, also mentioned immigration - in no uncertain terms.

“The speaker warned that unilateral action by the president on executive amnesty will erase any chances of doing immigration reform and will also make it harder for Congress and the White House to work together successfully on other areas where there might otherwise be common ground,” said the statement from Speaker Boehner’s office.

Earlier Friday, at a press breakfast hosted by The Christian Science Monitor, Republican National Committee (RNC) Chairman Reince Priebus called Obama’s pledge to take executive action on immigration “a nuclear threat to reject the basis of the separation of powers doctrine.” Later he likened it to “throwing a barrel of kerosene on the fire.” Mr. Priebus said Republicans would explore options to stop Obama’s move, both legal and legislative.

If Obama does press ahead with executive action on immigration, as promised, he will have presented Republicans with an exquisite dilemma.

To win the 2016 presidential election, the Republican Party must dramatically improve its performance among Latino voters. And to do that, it must get beyond the issue of immigration reform. That hasn’t happened, despite last year’s call by party leaders to “embrace and champion comprehensive immigration reform” in a report for the RNC on the party’s failures in the 2012 election.

Part of the problem, Priebus said at the breakfast, is that Republicans can’t agree on exactly what that means. But they do agree, he said, that US borders need to be secure before Congress can make any more moves on immigration – and bypassing Congress will only poison the president’s already tense relationship with Republicans.

At his post-election press conference on Wednesday, Obama said he needed to proceed with executive action on immigration, because he had made a commitment to do so. Then he aimed a message at Congress.

“You send me a bill that I can sign, and those executive actions go away,” the president said.

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Obama has faced intense pressure for months from Latino groups and immigration activists to provide relief for at least some of the 11 million people in the US illegally. His move in 2012 to defer deportations for people brought into the US illegally as children, but pressure soon grew to add more categories of people for deferred deportation. He had initially promised to make a move by summer of 2014, then delayed until after the election.

If Obama does take executive action deferring deportations, and Republicans try to undo it either in Congress or in court, that could deal a major blow to the GOP’s efforts to woo Latinos. What would follow is anybody’s guess, but there’s no doubt that Obama and the newly empowered Republican leaders in Congress are engaging in a high-stakes game of chicken.