U.S. President Barack Obama hosts a luncheon for bi-partisan Congressional leaders in the Old Family Dining Room at the White House in Washington, November 7, 2014. From L-R are Speaker of the House John Boehner, Obama, Senate Minority Leader Mitch McConnell. REUTERS/Larry Downing

In the wake of the last Tuesday's election, President Obama, incoming Senate Majority Leader Mitch McConnell and Speaker John Boehner all offered rhetorical bows to bipartisanship. But, a new post-election poll conducted by the Pew Research Center shows that two-thirds of Republicans have little interest in their top elected leaders trying to find common ground with the president.

Sixty six percent of Republicans said the they would prefer party leaders "stand up" to Obama "even if less gets done in Washington" while just 32 percent preferred GOP top brass "work with Obama, even if disappoints some GOP supporters."  That view stands in direct opposition to the view of the broader electorate on that question; 57 percent of all Americans prefer that Republicans work together with Obama while 40 percent favor GOP leaders standing up to the president. Among Democrats, a majority (52 percent) say that Obama should work with Republicans "even if it disappoints some Democratic supporters" while 43 percent would prefer they "stand up" to Republicans even if it means getting less done.

These numbers vividly paint the challenge before Congressional Republicans as they prepare to take over total control of Capitol Hill next year.  McConnell and Boehner -- longtime institutionalists -- undoubtedly will feel tugged toward trying to find some common ground with Obama in hopes of proving, on some small level, that they are not simply the opposition but can lead on a policy front too.  And yet, there is a clear majority of Republicans who have absolutely no interest in seeing their leaders cut deals -- large or small -- with the president.

In fact, the same Pew poll shows that almost six in ten (57 percent) of Republicans want their leaders to move in a "more conservative direction" while 39 percent want their leaders to move in a more moderate one. Some of that division is the result of the increasingly pejorative sense in which "moderate" is viewed among Republicans (it's becoming like "liberal" for Democrats) but the split also reflects the desire of the rank and file to confront a president for whom they -- and this is not too strong a word -- hate.

And, just in case you don't think the jobs of Boehner and McConnell in the 114th Congress will be hard enough, there will be an active fight for the 2016 presidential nomination playing out at the same time -- and in the halls of Congress. Texas Sen. Ted Cruz, who is moving aggressively toward a 2016 candidacy, has already made clear that his focus in the coming Congress will be to oppose Obama and roll back policies -- like the whole of the Affordable Care Act -- with which he (and the GOP base) disagree. (Cruz has also made clear he isn't sold on backing McConnell for Senate leader.)

Make no mistake: The 2014 election didn't end the fight between the conservative base and the GOP establishment. The party united to fight a common enemy. But, without that enemy on the ballot in 2016, the fight for the Republican nomination will be a battle between those two factions. And Boehner and McConnell will be caught right in the middle of it.