WASHINGTON (Reuters) - President-elect Donald Trump will enjoy Republican majorities in both chambers of Congress when he takes office in January and an early Capitol Hill honeymoon is likely on several issues, but a long-term romance may be more challenging.

Under normal circumstances, a president whose party controls both the Senate and House of Representatives can count on getting things done fairly quickly and Trump likely will not be an exception, but he will start with unusual handicaps.

Many Republicans in Congress only backed Trump after he became the nominee. Some never fell in line. He offended and attacked some while running, including House of Representatives Speaker Paul Ryan, who did not campaign with him.

On top of that, the New York real estate businessman and former reality television celebrity who will head the world's most powerful government and largest economy, has no governing experience.

"Donald Trump will lead a unified Republican government," Ryan told a news conference in his home state, Wisconsin, on Wednesday, promising to "work hand in hand" with him.

Ryan said his relationship with Trump "is fine" and he has already spoken to the president-elect twice, and to his running mate, Indiana Governor Mike Pence, a former House member.

Trump and the Republican leadership in Congress agree on at least one major policy: They want to repeal Democratic President Barack Obama's landmark healthcare law, known as Obamacare, enacted in 2010.

Ryan said Congress would move quickly to deal with the law.

Trump also spoke extensively about scrapping trade deals and building a wall along the 1,989-mile (3,200 km) U.S.- Mexico border, but some Republicans are skeptical about both of those campaign pledges.

INFRASTRUCTURE EARLY ON

In his victory speech, Trump promised to invest in infrastructure, a proposal popular with lawmakers from both parties, possibly funded by ending a law that lets corporations hold profits offshore without paying U.S. taxes on them.

Plans by House Financial Services Committee Chairman Jeb Hensarling, a Texas Republican, to rewrite banking law to ease regulations, and to limit powers of the Consumer Financial Protection Bureau, are likely to have smoother sailing.

"My hope is that President-elect Trump will focus on issues that unite us," Maine Republican Senator Susan Collins, an outspoken Trump critic, said in a statement.

Trump appealed to voters as a Washington outsider, at times leading his rallies in chants of "Drain the swamp," about the capital city.

But outside experts said the party leaders share enough of an agenda with Trump that they will move together as a group. Ryan credited Trump with turning his home state of Wisconsin to the Republican Party for the first time in decades.

Trump is "going to pursue every deal that can get done and there is a large possibility that Congress is going to work to go along, but also to get passed what they want," said Lara Brown, interim director of the Graduate School of Political Management at George Washington University.

Republicans kept control of both the House of Representatives and Senate, although Democrats cut slightly into their majorities. With a few races undecided, Republicans had secured 51 seats to Democrats 47 in the Senate.

That number could rise to 48. New Hampshire Governor Maggie Hassan, a Democrat, claimed victory in New Hampshire on Wednesday morning over incumbent Republican Senator Kelly Ayotte, although Ayotte said the race was too close to call.

COMMON GROUND ON OBAMACARE, TAXES

Repealing Obamacare would shake the U.S. healthcare and insurance industries, which have broadly called for measured reforms, although not for its full-scale elimination.

America’s Health Insurance Plans, or AHIP, a trade association that represents insurers such as Anthem Inc and Cigna Corp in Washington, said late on Tuesday that it would work with any new administration on the issue.

Trump has called Obamacare a "disaster" and vowed to repeal and replace it. House Republicans have already voted more than 50 times to repeal all or part of the law.

Senate Democrats were certain to fight an Obamacare rollback, but could be outmaneuvered by Republicans at the procedural level with Trump's cooperation.

"It would be a tragedy, and I certainly won't in any way cooperate or work with an effort to take health insurance away," Senator Angus King, a Maine independent who caucuses with Democrats, told CNN.

Trump and congressional Republicans will find common ground on taxes. Trump generally sees eye to eye with Republicans in Congress in calling for major tax cuts, including those for the wealthy, although details of their plans are not an exact match.

Trump has called for cutting the U.S. corporate income tax rate to 15 percent from the current level of 35 percent; Ryan's tax plan proposes going to 20 percent.

Trump and Ryan both back reducing the current number of tax brackets to three from seven. Trump supports lowering the top individual income tax rate to 25 percent from 39.6 percent, while Ryan wants it to go to 33 percent.

Congressional Republicans likely would welcome a move by Trump to rescind some of Obama's executive actions on immigration, labor rights, the environment and global warming.

Virginia Republican Representative Dave Brat said one thing he expected Trump to do early as president would be “taking a pen to all of Obama’s executive overreach. ... That’s a quick, easy fix to get the regulatory burden down."

Trump has also said he wants to do some things as president, such as ban Muslims from the country and allow torture in the fight against terrorism, that some experts say are legally questionable.

By Susan Cornwell and Richard Cowan

(Additional reporting by David Morgan, Ian Simpson and Patricia Zengerle; editing by Peter Cooney and Grant McCool)

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