Obama, McConnell talk cooperation. This big issue may derail that.

President Obama and soon-to-be Senate majority leader Mitch McConnell both said nice things yesterday about the need to work in a bipartisan manner to govern the United States.

But it’s also clear that before New Year’s Day 2015, congressional Republicans and the White House are likely to be engaged in a policy battle that promises to be one of the most bitter and divisive fights of the entire Obama era.

The subject: immigration.

During his post-midterm press conference Wednesday, Mr. Obama indicated he’s not backing off his promise to take some sort of unilateral action on immigration, soon. He said that Congress hasn’t taken action, so he will.

“Before the end of the year, we’re going to take whatever lawful actions that I can take, that I believe will improve the functioning of our immigration system, [and] that will allow us to surge additional resources to the border, where I think the vast majority of Americans have the deepest concern,” said Obama.

This contradicts those pundits who felt Obama might delay or cancel such an action due to the shellacking Democrats received on Election Day. “Meet the Press” host Chuck Todd, for instance, said Tuesday night that the midterm results should put an end to Obama’s long-discussed unilateral immigration move.

“The president is going to know that if he does this, he is starting a war,” said Mr. Todd during MSNBC’s election coverage.

Senator McConnell (R) of Kentucky said pretty much the same thing during his post-victory press appearance. He indicated that if Obama did indeed ease the threat of deportation for millions of migrants present in America illegally Republican lawmakers would be outraged.

“It’s like waving a red flag in front of a bull to say, ‘If you guys don’t do what I want, I’m going to do it on my own,’ ” said McConnell in his Louisville news conference.

So what’s going to happen?

First, the degree of confrontation will depend crucially on what Obama actually does (duh). If he takes some pro-forma action meant to placate Hispanic groups that have been pushing him to move, the GOP will be far less exercised than if he grants what they would consider widespread amnesty to illegal immigrants.

Second, the degree of confrontation will further depend on what happens within each party, as much as between them.

Obama’s getting pressure from progressives and Hispanic groups to do as much as possible. Some even insist that the mid-term losses would have been eased if the White House had already acted, since Hispanic turnout might have been higher in such states as Colorado, where incumbent Democratic Sen. Mark Udall went down in defeat.

“Advocacy groups like Presente and the National Day Laborer Organizing Network (NDLON) have actively called on Latinos, who were a decisive force in the 2012 election, to resist voting for Democrats out of anger that the president hadn’t acted on promised action,” writes Esther Yu-Hsi Lee on the left-leaning Think Progress site.

McConnell arguably faces even more intense internal push-back. Conservative groups are livid that the Kentucky senator in his Wednesday appearance promised that he wouldn’t shut down the government or threaten to default on the national debt in an effort to get Obama to do what Republicans want.

The headlines from some popular right-leaning sites said it all. “McConnell Should Defund the White House if Obama Tries Amnesty,” wrote Breitbart.com. “Republican Majority, Day One: McConnell Surrenders,” wrote RedState.

Thus McConnell’s reputation as a shrewd political and legislative strategist may face its toughest test even before he takes his new office. Because that’s one of the obvious advantages of the president’s timetable: If he moves before the end of the year, Democrats will still control the Senate. The new Congress won’t be sworn in until the first days of January 2015. McConnell will have to wait before he can exercise actual power in response to whatever Obama does.

Much depends on what happens, for those who might be affected by changes in US immigration policies, and for Congress as well.

A bitter battle over this contentious issue could ruin chances for bipartisan compromise on even small issues and pitch the parties that govern America into static trench warfare for the remainder of Obama’s time in office.