Republicans also will have to navigate internal battles over how aggressively to challenge Obama as they confront years of pent-up policy demands from their base.

"The president and the Republicans are going to each have a choice to make: Do they move to the center to get things done or do they stay true to their respective bases," said Jim Manley, a former aide to Senate Majority Leader Harry Reid, a Nevada Democrat.

'An obligation'

Senator Mitch McConnell, who won his re-election race and is poised to become majority leader in January, said in his acceptance speech last night that he and Obama have "an obligation to work together" on issues where they can agree.

McConnell plans to hold a news conference at 2 p.m. today in Louisville, Kentucky. Obama has scheduled a news conference at 2:50 p.m. Washington time.

The president invited the four current top leaders in Congress to the White House for a meeting on Nov. 7.

Republican Senator-elect David Perdue of Georgia said on Fox News today he'll bring a "fresh perspective" and wants to address the corporate tax rate, repatriation of overseas corporate profits. In addition, "we want to get this energy resource unlocked," he said.

Keystone pipeline

Republican control of the Senate improves the prospects for issues where some Democrats already agree, such as the Keystone XL pipeline, repeal of a medical-device tax and fast-track trade authority.

Issues that split Republicans, such as changes to tax and immigration policy, are likely to remain at an impasse, as they have since Republicans took control of the House in 2011.

"It's difficult to imagine significant legislative progress on any initiatives," said Isaac Boltansky, an analyst at Compass Point Research & Trading in Washington. "We should have tempered expectations about what can actually be accomplished."

Republicans needed to win a net six seats for the majority and picked up at least seven in West Virginia, Montana, Arkansas, South Dakota, Colorado, North Carolina and Iowa. Louisiana will go to a run-off, as neither candidate won more than 50 percent of the vote.

Lame-duck session

The win buoys Republicans in the short term, giving them a new edge in negotiations during Congress's lame-duck session that starts next week. Democrats will control the Senate until early January as the parties face a Dec. 11 deadline for the lapse of government funding and try to revive dozens of tax breaks that expired at the end of 2013.

Reid issued a statement last night congratulating McConnell on succeeding him as majority leader and casting the election as a mandate for compromise.

"The message from voters is clear: They want us to work together," the Nevada Democrat said.

At the start of 2015, Republicans will get to set the Senate agenda. They'll be under competing pressures.

The party's most hard-line members, including Texas Sen. Ted Cruz, will want to go on the offensive against Obama, pushing bills to repeal Obamacare, cut government spending and limit regulation.

'Pare back'

"We're going to see some effort to pare back Obamacare," said John Pitney, a political scientist at Claremont McKenna College in California. "Outright repeal might not be practical, but Republican voters expect some action on the issue because the party's been talking so much about it."

Republicans in October 2013 forced a 16-day partial government shutdown over demands for limits on Obamacare in exchange for funding federal operations. Some conservative groups have criticized McConnell, saying the Kentuckian hasn't committed strongly enough to repealing the health care law.

Other Republican lawmakers, looking ahead to the 2016 election, will be looking for bipartisan achievements. Among the possibilities are approving the Keystone oil pipeline, repealing Obamacare's medical-device tax and granting Obama fast-track authority.

Those issues have broad Republican support and attract some Democratic votes in the Senate because of home-state concerns. Democrats such as Heidi Heitkamp of oil-rich North Dakota back Keystone. Democratic lawmakers who represent clusters of device makers, including Amy Klobuchar of Minnesota, oppose the medical device tax.

Obama deciding

A bipartisan group of lawmakers already has been trying to force a Senate vote to approve the Keystone pipeline. Reid, who sets the chamber's agenda under Democratic control, refuses to bypass the Obama administration, which is deciding whether to let the project move forward.

Earlier this year, pipeline supporters said they had backing from 56 senators, including all 45 Republicans, though still four shy of the 60 needed to advance the bill. The House has passed similar measures by broad majorities.

Companies including Becton Dickinson and Co. and Medtronic Inc. are lobbying for repeal of the 2.3 percent excise tax on medical devices that aren't sold directly to consumers. The tax was enacted to help pay for Obama's Affordable Care Act.

Republicans may be able to use must-pass bills to win concessions from Obama. McConnell has said he wants to attach provisions to spending bills that would curtail regulations affecting coal-fired power plants.

AFL-CIO president

AFL-CIO President Richard Trumka, at a news conference in Washington today, credited the Republicans for having a strong focus on the economy.

"It's not the people, it was the message," Trumka said. "Tell us how you're going to solve our economic problems. And unfortunately they heard more of that from Republicans."

Control of Congress doesn't grant absolute power and in many cases, it will shift the divide, not eliminate it. The Senate's procedural rules that require 60 votes to advance most legislation, as well as the presence of Obama in the White House, will limit what Republicans can do.

Obama can veto any bill, and it would take two-thirds of the members in both chambers to override him. If the president maintains support among congressional Democrats, Republicans will have to negotiate with him rather than stampede over him.

The Senate in particular would need a bipartisan approach, as 60 votes are needed to advance most major bills.

"If the leadership decided hey, we are ready to enter into negotiations with this president to get something done, that would change the dynamic," said Kent Conrad, a former Democratic senator from North Dakota.

Breaking gridlock

"If instead they cling to the position they've been holding, which is they don't deal with this president on anything," little will happen besides posturing, Conrad said.

The one potential way to break through this gridlock is through what is known as reconciliation. That's a procedure that lets the Senate pass bills by a simple majority, and without delaying tactics by the minority party.

One of the first planning meetings between McConnell and House Speaker John Boehner, an Ohio Republican, most likely will include "a debate about reconciliation and what they intend to do," Manley said.

Though being able to use reconciliation isn't a given. The House and Senate would have to adopt identical budgets and then return with follow-up legislation.

This procedure may be reserved for the most partisan bills they want to send Obama to make a statement, because anything that passes on a razor-thin margin also would probably draw a veto threat.

'Clear demarcation'

A veto would "present a clear demarcation of the differences between the agenda of the Republicans and the agenda of the president," said former Arizona Senator Jon Kyl, who was the chamber's second-ranking Republican before leaving Congress in 2013.

Republicans also will have disagreements among themselves as they try to forge party unity. Party members in the Senate cover a wide range of ideological positions, from the small- government absolutism of Cruz to the conciliatory approach of Maine's Susan Collins.

Boltansky said lawmakers may be able to agree on some changes in financial regulation, including easing rules for regional and community banks and a capital-formation bill that would aid middle-market companies.

"The political climate for the nation's biggest banks isn't going to improve; in fact, it's likely to worsen," he said. "It seems like the one bipartisan issue on Capitol Hill is big-bank bashing at the moment."

With assistance from Kathleen Miller in Washington.

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