The question is how much of the GOP's government-shrinking, tax-cutting agenda to advance, and how fast.
It's certain that Republicans want to capitalize quickly on tea party-fueled anger and the antiestablishment fervor that they believe will provide momentum to accomplish an activist to-do list. It's equally clear, however, that the outsized expectations of a fed-up electorate and a crop of unruly newcomers could complicate the plans. So could Mr. Obama and fellow Democrats who will still be around after Tuesday's elections.
GOP lawmakers are publicly mum about much of what they intend to do if they prevail in midterm congressional contests. Many say privately they want to avoid appearing to "measure the drapes" for new leadership offices before winning any majority.
But especially in the House - where Republicans have a clear shot at scoring the 40-seat gain they would need for control - they are in intense internal talks about how a GOP-driven agenda would work.
In the latest CBS News/New York Times poll,(46 percent to 40 percent) among of likely voters - a gap largely driven by GOP-leaning independents.
Rep. John Boehner, in line to become speaker under that scenario, and Rep. Eric Cantor, his No. 2, have had initial discussions to ensure a plan is ready, a spokesman said.
Most agree a marquee item on a new GOP majority's agenda would be an aggressive package of spending cuts, on the order of $100 billion or more, that could also be paired with steps to block implementation of key parts of Mr. Obama's health care law and new financial regulations.
What's less clear is how Mr. Obama would respond, and whether a turbocharged Republican majority could muster a bipartisan compromise, especially when its freshman class will probably have little appetite for following any established party position or leader.
"The Republican Party is still a tattered brand. It's not as if people are enthusiastically embracing the Republican brand - they're rejecting what has been done the last two years," said Michael Franc of the conservative Heritage Foundation, a House aide following the 1994 Republican takeover. "They're going to have to do something that is dramatic enough to say to people, 'We heard you."'
GOP leaders are working to calibrate expectations, Franc said, so they don't end up being accused of "being a fiscal squish" if they compromise on cuts.
Republicans laid out some of their wish-list last month in the "Pledge to America," which called for tax and spending cuts, health care law repeal and congressional reform, among other things. Some GOP leaders argue a victory on Election Day would give them a strong mandate to carry out such changes, although many of them are likely to run into strong Democratic opposition.
"If the public puts us in the majority, they're saying that they want this to go forward," said Rep. Kevin McCarthy, R-Calif., one of the pledge's architects.
Mr. Obama, he added, "would be in a hard position not to support this."
That's not necessarily a view shared by the Senate's top Republican, Mitch McConnell of Kentucky, who'll have a vital role leading a strengthened GOP team in that chamber, regardless of whether the party reaches the long-shot goal of gaining the 10 seats necessary to get control.
"I think humility and gratitude is the appropriate response to the midcourse correction that I think is coming - not, you know, sort of chest-beating or spiking the ball in the end zone or acting like we have been entrusted with the entire federal government," McConnell said in a recent interview. A win on Nov. 2, he added, would be "a good first step toward turning the government back in the direction that I and virtually everybody in the country aligned with our particular point of view think is ... necessary."
On both sides of the Capitol, Republicans know they face a difficult task - scarcely less daunting than Obama's own after he was elected president - in fulfilling the expectations of angry voters who are once again demanding change.
Much depends on how Mr. Obama would choose to work with a GOP majority. Clashes are virtually guaranteed over spending cuts, as well as Republican attempts to permanently extend income tax cuts not only for middle-income people, which Democrats support, but for the highest earners too.
McCarthy said the president should "realize the election's over, realize the message the voters have sent and maybe go study what Bill Clinton did," moving to the right to meet Republicans.
First-termers who ran as enemies of business-as-usual in Washington aren't likely to be in the mood to accept the standard bargaining that's virtually certain to result once their colleagues on Capitol Hill and outside interest groups - including the business lobby - get a look at the GOP's proposals.
"They come in with an authenticity that nobody has: 'We were elected in the year of the tea party. We know what the people want. You are just old fuddy duddies who have been here forever and are part of the problem,"' said Grover Norquist, the president of Americans for Tax Reform who often advises congressional Republicans.
On health care, there's little doubt that a Republican majority would quickly set a vote to ax the overhaul law - a symbolic move that has no chance of succeeding given Obama's veto pen. The GOP would then follow up with attempts to block key elements of the measure by denying the money to implement it.
But there are internal rifts over which portions to leave alone and which to target, with some conservatives predisposed to block as much of the law as possible and others worrying about obliterating politically popular elements.
"The class of '94 was rambunctious, but not as rambunctious as this class is likely to be. Herding these cats is going to be more difficult than usual," said John Feehery, a former senior House aide who helped keep the new GOP majority in line behind the "Contract with America" following the 1994 election.
Republican leaders, hoping for another such sweep after two consecutive losing elections, say potential intraparty rifts don't scare them.
"I can tell you it's a problem I'd love to have," McConnell said. "I'd rather be the leader of more people than fewer people."