Facing a new political landscape, President Barack Obama and Sen. Mitch McConnell had a Wednesday appointment to size up prospects for cooperation between Democrats and Republicans who have shown little zest for political deal-making in the more than five years since Obama's first inauguration.

The Oval Office talk was the first one-on-one meeting between Obama and the Kentucky Republican since the GOP took control of the Senate in November's midterm elections. McConnell, who famously asserted after Obama's January 2009 inauguration that his goal was to make Obama a one-term president --is now poised to become Senate majority leader when the new Congress convenes next month.

Obama and McConnell have both spoken about their interest in cooperating where possible -- in areas like tax reform and infrastructure investments -- although working through the details of legislative proposals is sure to expose long-standing divisions on issues. The president's decision to move forward on an administrative remedy for immigration problems has infuriated some Republicans, who urged the president to hold off on the moves following his party's sweeping defeats at the polls.

McConnell said Tuesday that he had been "perplexed" by Obama's reaction to the election.

"I don't know what we can expect in terms of reaching bipartisan agreement," he said. "That's my first choice, to look at things we agree on -- if there are any."

Speaking to a group of business leaders Wednesday, ahead of his meeting with McConnell, Obama said he wanted to discuss with both McConnell and House Speaker John Boehner their priorities for the congressional agenda in 2015. But he said one of his priorities would be to quickly start discussions on overhauling the nation's complex tax laws.

"There definitely is a deal to be done," Obama said, adding that he hoped to get that process started quickly next year "because you need a pretty long runway on that. It takes some time."

The president also suggested that there was still an opportunity to pursue immigration legislation on Capitol Hill. He predicted that Republicans would first "take a couple stabs at rolling back" his executive actions, then start weighing potential legislative action.

However, the president also said he didn't expect that to happen quickly given the anger over his directives to delay deportations, allowing more than 4 million people in the U.S. illegally to stay here and get work permits.

"Temperatures need to cool a bit in the wake of my executive action," he said.

On Capitol Hill, some Republican lawmakers remained skeptical of the prospects for bipartisan agreement, but said the mere fact that Obama and McConnell were meeting 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.