WASHINGTON (AP) — In a rare one-on-one meeting, President Barack Obama and incoming Senate Majority Leader Mitch McConnell on Wednesday sized up the prospects for bipartisan cooperation between a White House and Republican Party that have struggled for years to find common ground.

Ahead of the Oval Office meeting, Obama outlined his most specific blueprint yet for striking compromises with Congress when the GOP takes full control of Capitol Hill next month. The president said there was “definitely a deal to be done” on overhauling the nation’s complicated tax code, but suggested it could take lawmakers more than six months to iron out the details of such an agreement. He said a deal on infrastructure spending could be included in a tax overhaul package and predicted progress on overseas trade agreements.

On immigration, Obama said he expected Republicans to attempt to dismantle his recent executive orders, then eventually come around to the idea of pursuing legislation to deal with the millions of people in the U.S. illegally.

“I don’t think that’s something this Congress will be able to do right away,” Obama said during a question-and-answer session with business leaders. “Temperatures need to cool a bit in the wake of my executive action.”

McConnell, the Kentucky lawmaker who is soon to become Senate majority leader, has broadly agreed with Obama’s calls for tax reform, improving the nation’s infrastructure and inking free trade pacts. But McConnell said Tuesday that he has been “perplexed” by Obama’s response to his party’s sweeping defeats in the midterm elections last month, specifically his decision to press forward with presidential directives on immigration.

“I don’t know what we can expect in terms of reaching bipartisan agreement,” McConnell said. “That’s my first choice, to look at things we agree on — if there are any.”

Neither McConnell nor Obama spoke publicly after their hour-long meeting Wednesday. A spokesman for McConnell called the sit-down “a good meeting” but offer no further details.

The two men have a chilly relationship, with McConnell once asserting that his goal was to make Obama a one-term president.

The senator’s office said Wednesday’s meeting marked just the third time the two men have met face-to-face without other lawmakers. They met one-on-one in 2010 and held another discussion in June 2011, a meeting Vice President Joe Biden also attended, according to McConnell’s office.

The day after Democrats’ defeats in the midterm elections, the president suggested he would be open to more personal time with McConnell.

“I would enjoy some Kentucky bourbon with Mitch McConnell,” said Obama, who last year mocked the idea of having a drink with the GOP leader. Then, offering a glimpse into how little time Obama has spent cultivating a relationship with McConnell over the past six years, the president added, “I don’t know what his preferred drink is.”

Aides said there was no bourbon consumed in the Oval Office Wednesday. In an interview with Yahoo News ahead of the meeting, McConnell said, “Drinking bourbon in the middle of the afternoon would not be good for either of our careers.”

On Capitol Hill, some Republican lawmakers remained skeptical of the prospects for bipartisan agreement, but said the mere fact that Obama and McConnell met face-to-face was a positive step.

“At least they’re doing something that they didn’t do, as I understand it, the first couple of years,” said Sen. Roy Blunt, R-Mo.

Sen. Bob Corker, R-Tenn., said that while Obama’s relationship with Republicans “started out in a not positive way,” the GOP would have to seek ways to work with him over the next two years.

“The fact is he is the president who the people of our nation elected to work with over the next couple of years,” Corker said. “If you want to get big things done, he’s got to be involved.”

While much of Washington’s focus following the election has been on Obama’s relationship with the GOP, the president also faces tests in bringing his own Democratic Party along on some of his top priorities for 2015. He’s particularly at odds with his party on free trade agreements, which some Democrats see as harmful to American workers.

During his remarks to business leaders, Obama implored Democrats to drop their opposition to pending deals with Europe and Asia.

“Don’t fight the last war,” he said. “Those who oppose these trade deals ironically are accepting a status quo that’s more damaging to American workers.”

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