Which Republican party will show up on Capitol Hill in January, when the GOP assumes control of the Senate?

Will it be the party of "yes," which takes responsibility for being part of the governing process? Or will it be the party of "no," which simply opposes anything President Obama favors?

How Republicans answer that question will make a huge impact on two critical issues: 1. What happens during Obama's last two years in office? 2. Will their party be able to elect a president of their own in 2016?

Republicans ran a smart campaign that effectively captured the mood of dismay and dissatisfaction -- even fear -- pervading the country. On election night, 71 percent said they were worried about a terrorist attack; 74 percent viewed the direction of the economy negatively; only 22 percent said the next generation would be better off than they are.

As former senator John Breaux cogently put it, the GOP campaign could be reduced to two words: "Obama bad." A brilliant bumper sticker, but hardly a platform for exercising power. And other numbers should send warning signals to the Republicans.

Only 36 percent of voters viewed the Republican party favorably. In a CBS poll on the eve of the election, only 21 percent approved of the way Republican lawmakers were doing their job.

In a Wall Street Journal/NBC survey, 36 percent of voters listed "ending gridlock" and "getting things done" as the main issues influencing their vote for Congress. Only job creation and economic growth ranked higher.

Republican leaders in the Senate seemed to take that message of conciliation seriously. Mitch McConnell, who survived a stiff electoral challenge in Kentucky and will become majority leader in January, said in his victory speech that Republicans had an "obligation" to cooperate with Democrats "on issues where we can agree."

His deputy, John Cornyn of Texas, told the Wall Street Journal that voters wanted Republicans to demonstrate that they can "actually govern." Party leaders understand that "people want government to function, whether you're a conservative or a liberal."

That's exactly what most voters in both parties want from government: value for their tax dollars. And Team Obama evinces some optimism that the governing caucus will set the Republican agenda on Capitol Hill.

"Going into 2016, the Republicans have to make a decision whether they're in control or not in control," Vice President Biden said on CNN. "Are they going to begin to allow things to happen? Or are they going to continue to be obstructionists? And I think they're going to choose to get things done."

As for the White House, Biden added: "We're ready to compromise."

Healthy skepticism is required here. We've heard these words before, many times, from both sides. Politicians pander to this yearning for pragmatism in their public statements, but when the time comes for compromise, for making hard choices that might anger their core supporters, they revert to bare-knuckle partisan warfare.

No wonder Congress' favorability rating is 12.7 percent. Even ISIS might be more popular.

Here's the problem for the GOP: McConnell, Cornyn and Co. might well understand what the public wants from their party. But they don't "control" the conservative ideologues led by Sen. Ted Cruz of Texas, who equate any whiff of compromise with heresy.

In an interview with the Washington Post, Cruz would not even promise to support McConnell for party leader and advocated a Holy War that includes trying "every means possible to repeal Obamacare."

Combat, not conciliation, is his game plan. That way, Cruz said, "You have clear accountability. It becomes transparent to everyone that it is the Democrats blocking meaningful progress."

Cruz's strategy might not prevail in the Senate, where lawmakers have to run statewide and several Republicans face tough re-election races in blue states in 2016. But the Texan has already shown a willingness and an ability to rally House members -- who are insulated from political accountability by their deep-red districts -- to his No Compromises banner.

As a result, Speaker John Boehner has tried and failed on many issues -- such as immigration and deficit reduction -- to muster his party's support for a governing strategy that includes the kind of cooperation with the president that McConnell is suggesting.

So the stage is set. In the fight to define the Republican Party, will the forces of "yes" prevail, or the forces of "no"? Will the GOP enter the next presidential election as the party that gets things done? Or the party that's given up trying?