Rep. Paul Ryan (R-Wis.) (AP Photo/Steve Helber)

Facing the prospect of a fully Republican Congress for the first time in eight years, GOP strategists are divided over how to advance a central tenet of their political agenda: a simpler U.S. tax code with sharply lower rates.

In the House, Republicans weary of jousting with President Obama over sweeping tax and budget issues say they have little hope of suddenly finding consensus in the waning days of his administration. Better, they argue, to focus on smaller targets, such as approving the Keystone XL Pipeline and rolling back broadly unpopular pieces of the Affordable Care Act, such as a tax on medical devices and cuts to Medicare Advantage.

In the Senate, however, aides and advisers say a newly-elected Republican majority may be more inclined to aim for much bigger prizes. Among the prime options: A far-reaching tax code rewrite -- if not for individuals, then at least for U.S. businesses, which currently labor under the highest corporate tax rate in the developed world.

Such ambitions would depend heavily on Obama, Republicans say; they would go nowhere unless the president, too, were determined to cut a deal. The White House has long called for lower taxes on business, a call that has become more urgent this year as a steady stream of firms has fled overseas.

With another deadline looming next spring to lift limits on federal borrowing, some GOP strategists see a faint path to significant legislation that would raise the debt ceiling through Obama’s presidency, cut taxes and let all sides claim victory.

For the moment, those discussions are proceeding quietly while Washington awaits the outcome of the Nov. 4 elections. Several races are too close to call, and if runoffs are required in Louisiana or Georgia, control of the Senate could be in doubt until as late as January.

Meanwhile, the GOP’s most important tactician, Senate Republican Leader Mitch McConnell (Ky.), has been more focused on the fight to keep his own Senate seat from challenger Alison Lundergan Grimes (D) than on mapping post-election strategy.

Further muddying the outlook: If Republicans do win the Senate, their margin of control is expected to be slim, meaning they would need help from Democrats to clear the 60-vote hurdle typically required to pass major legislation. And it’s not clear that Democrats would play along.

Sen. Charles E. Schumer (D-N.Y.), a member of Democratic leadership and a senior member of the tax-writing Senate Finance Committee, has all but ruled out a major tax bill in the final years of the Obama administration.

Schumer recently offered a proposal to make it less lucrative for corporations to move their headquarters abroad, a maneuver known as “inversion,” suggesting that it could serve as a bridge to farther-reaching reform -- in 2017.

“I think it will be hard to get tax reform in the next two years,” Schumer said.

Even the perennially optimistic Sen. Ron Wyden (D-Ore.), the author of two bipartisan tax reform proposals and the current chairman of the Senate Finance Committee, is making no promises.

“Until about a year from now” – when the 2016 presidential campaign will begin to “suck all the oxygen out of the room” – “I think there’s a prime opportunity to do big important stuff,” Wyden said. But he added: “I’m not telling people there’s a 95 percent chance it’s going to get done.”

Sen. Orrin Hatch (R-Utah), who would ascend to the Finance Committee chairmanship in a Republican Senate, and Rep. Paul Ryan, who is favored to chair the tax-writing House Ways and Means Committee next year, have been equally noncommittal.

“We don’t know how much progress we’ll make on those issues,” Ryan (R-Wisc.) recently told the Financial Services Roundtable. “Tax reform’s one of those things where we just don’t know if we can get there at the end of the day.”

Still, Republicans would be under intense pressure to take a shot at a major tax bill if they held control of both chambers of Congress, aides said.

A 25-percent top tax rate (down from the current 35 percent for corporations and 39.6 percent for individuals) is a centerpiece of the GOP agenda. And American business is growing increasingly impatient with the lack of action on the corporate code, which imposes the highest rate among advanced economies and is the only system that taxes overseas profits.

“To the extent that U.S. businesses could anticipate meaningful tax reform, these inversions would taper off very quickly,” said Randall Stephenson, chief executive of AT&T and chairman of the Business Roundtable, an organization of corporate chief executives. “We have the most uncompetitive tax system in the developed world. As a result, companies are doing what you would expect them to do as rational actors.”

Ryan may be laying the groundwork for proceeding alone, without Democratic support: In his speech to the Financial Services Roundtable, Ryan suggested changing the rules by which the nonpartisan Congressional Budget Office judges tax bills by requiring the agency to take into account any positive effects on the overall economy. That process, known as “dynamic scoring,” could make it easier for Republicans to write legislation that cuts taxes without expanding budget deficits.

But Democrats oppose dynamic scoring, and moving legislation without their support could be perilous. As retiring Ways and Means chairman Dave Camp (R-Mich.) demonstrated when he unveiled his own tax reform package last this year, significantly reducing rates would require new limits or repeal of many popular tax breaks. With 23 seats up in 2016, Senate Republicans might view such tough medicine as a sure ticket back to the minority.

Camp has pressed mightily for bipartisan cooperation. Last year, he worked closely with Max Baucus, the Montana Democrat who chaired the Senate Finance Committee until Obama selected him as ambassador to China. More recently, Camp has been calling on the White House to lay its cards on the table.

“We need a plan. We need a proposal from the administration,” Camp said. “And we have not had that in the four years that I have been chairman.”

Could Obama and Republicans find common ground for tax reform? The Democratic think tank, the Center for American Progress, recently released a report outlining areas of overlap between Camp’s plan and ideas offered by the administration. Among them: Eliminating accelerated depreciation and enacting a bank tax.

The bipartisan Committee for a Responsible Federal Budget cheered the report in a blog post titled, “Finding consensus on tax reform.” But the post added, with significant understatement:

“While the President's budget and Camp draft have a number of policies in common, they take place in different contexts. President Obama uses revenue increases to pay for other priorities (spending increases and tax cuts) and reduce the debt. Camp uses these base-broadeners to finance rate reductions in revenue-neutral tax reform… The original authors of the proposals may not agree with each option being used in a different context.”

And that gets to the heart of the primary problem with tax reform: Democrats want it to produce more revenue for government programs and to reduce the deficit; Republicans refuse to “raise taxes.”

A bipartisan package could focus exclusively on corporate and business reform, where both sides say they want a new code that raises roughly the same amount of money as the current system. The White House has been encouraging this approach.

But many Republicans reject the idea of providing tax relief to corporations without helping individuals and the smallest businesses. Wyden, for one, thinks they’re right.

“I don’t think you can have tax reform,” he said, “where the big guys get the breaks and the little guys get nothing.”