President Obama firmly rejected advice from top congressional Republicans on Friday that he delay his promised executive action on immigration reform, dismissing calls from critics inside and outside his party to allow Congress to debate the issue next year.

Over a two-hour lunch of Bibb lettuce salad, herb-crusted sea bass and pumpkin tart, House Speaker John A. Boehner (R-Ohio), Senate Minority Leader Mitch McConnell (R-Ky.) and their lieutenants warned Obama that his acting alone on immigration would spoil chances for bipartisan agreement on other issues in the new GOP-controlled Congress.

Seated with 12 top members of the House and Senate in the Old Family Dining Room, Obama shot back that he intended to proceed, saying that he had already waited almost two years for congressional action on immigration. He added that his decision should not upend chances for cooperation on unrelated matters, according to aides familiar with the exchange.

The new focus on Obama’s plans to revamp the immigration system by executive fiat came as the president is reportedly reviewing proposals to allow as many as 5 million illegal immigrants to stay in the United States at least temporarily, according to several people familiar with his plans. He is expected to announce his intentions after returning from a visit to China, Burma and Australia, either this month or in early December, said those familiar with the subject, who spoke on the condition of anonymity because they were not authorized to speak publicly on the matter.

Obama’s immigration pledge became political grist for Republican congressional candidates, who opposed his decision to act unilaterally. And after a dismal Democratic showing in the midterm elections Tuesday, David Axelrod, a former Obama adviser who remains close to the president, suggested via Twitter that Obama should “shelve” his plans to take action in hopes of an “up or down vote” in the House.

But congressional Democrats and immigration-reform activists insisted that Obama will proceed. Some have expressed regret that he has not already acted.

“He should do it. . . . Just get it done,” said Rep. Joe Garcia (D), a first-term lawmaker who lost reelection on Tuesday in his South Florida district.

Garcia lost to Carlos Curbelo, a Miami-Dade County School Board member who snatched back a seat that Republicans lost two years ago. In an interview, Garcia said that instead of settling the immigration issue by taking action, Obama had allowed “a sustained, continuous conversation” among Democrats to fester, exposing intraparty divisions.

“Republicans not only were bad on immigration at the beginning of the year, they were bad during the year, they were bad at the end of the year,” Garcia said. “At the same time, we’re being woodshopped for not moving on the executive order, and that’s why he should have just done it.”

White House press secretary Josh Earnest said Friday that Obama “is very focused on” immigration and that Republicans can do only one thing to stop him.

“They can allow that common-sense, bipartisan bill from the Senate to come to the floor of the House of Representatives,” he said. “And if the House passes that Senate bill, the president won’t take executive action. Maybe the republic will be saved. Maybe the ego of the House Republicans will not be bruised. Certainly, the United States of America would benefit significantly from them taking that step.”

Earnest was referring to a 2013 Senate bill passed with bipartisan support that would make sweeping changes to the nation’s immigration and border-security system. But Boehner and House Republicans rejected the measure.

Boehner did not rule out introducing immigration legislation if Obama decided not to act. “This immigration issue’s become a political football over the last 10 years or more. It’s just time to deal with it,” he told reporters this week.

On Friday, aides to Boehner played down published reports that the speaker had held secret talks on immigration with Obama since after the 2012 election.

“There was no negotiation; there was no substantive conversation,” said a senior GOP aide familiar with the exchanges. Instead of immigration-specific meetings, the subject came up several times during meetings or phone calls between the two on other matters, the aide said.

Even as Republicans remain divided on what to do about immigration, there appears to be unanimity among them that Obama should not get involved until legislation has been passed.

“Surely he has someone around him who can communicate to him how tone deaf it would be for him to act by executive order,” Sen. Bob Corker (R-Tenn.) said in an interview Friday. “Surely he understands how divisive that is and how it really would start us off in exactly the wrong place.”

The chairman of the Republican National Committee also warned Obama on Friday against taking executive action. Speaking at a Christian Science Monitor breakfast with reporters, RNC head Reince Priebus said that if the president signs an “executive amnesty” order, he will be “throwing a barrel of kerosene on a fire.”

But congressional Democrats dismissed the GOP warnings.

Sen. Patrick J. Leahy (D-Vt.) said in a statement Friday, “If Speaker Boehner actually wants to boost the American economy, he could do that next week by taking up the bill we passed a year and a half ago.”

Sen. Charles E. Schumer (D-N.Y.), an architect of the Senate’s bipartisan bill, agreed. If House Republicans fail to act by the end of the year, “the President will have no choice but to fix parts of our broken immigration system where he is legally allowed,” Schumer said in a statement.

Frank Sharry, founder and executive director of America’s Voice, a pro-immigration reform group, said that Obama risks his legacy and the Democratic Party’s appeal to Latinos if he does not act soon.

“A disappointed Latino electorate did not help the Democrats as much as they could have this year, and an enthusiastic Latino electorate could spell the difference in a number of states in 2016,” he said. “Given the 2016 map, it’s advantage Democrats, but not if they continue to dis a core constituency.”

Juliet Eilperin and Sean Sullivan contributed to this report.