The nation's new, all-Republican leadership begins to take the reins of power Tuesday promising to cut taxes, roll back regulations and undo President Barack Obama's signature health law -- but with a complicated path for enacting its agenda and important policy details still undetermined.

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After new senators are sworn in Tuesday by Vice President Joe Biden, a symbol of the departing Democratic administration, and House members by Speaker Paul Ryan, the Republicans among them plan to move quickly to turn back an era defined by Mr. Obama's ambitions to make the government a more powerful force in the economy.

Republicans will hold the White House and both chambers of Congress for the first time since early 2007 once President-elect Donald Trump is sworn in Jan. 20, creating high expectations within the party that it can enact long-held policy goals. When Mr. Trump met recently with Sen. David Perdue (R., Ga.), "all we talked about for the better part of an hour was how to get results in the first part of the year," Mr. Perdue recalled.

One of the first goals for Republican leaders is to dismantle the Affordable Care Act, which they say hurts quality and choice in health care. The Senate's opening move, coming as soon as Tuesday, will be to initiate a controversial process to repeal the law, which has brought health insurance to more than 19 million people but has taken a hit as the number of insurers offering coverage has shrunk and premiums have jumped.

As with many of the Republican goals, the effort is creating a maze of challenges. The most pressing is how to develop a replacement for the 2010 health law without triggering the sort of disruptions that accompanied the law's rollout, which in turn contributed to the Democrats' loss of their Senate majority in 2014.

Many health insurers have stopped writing policies under the law, leaving insurance markets struggling in some states, including GOP-leaning Arizona, Alaska and Tennessee. Some Republican lawmakers, whose votes will be crucial to any repeal-and-replace plan, are worried that a repeal would yank the rug out from under people who need coverage.

Republicans also know that a confirmation hearing for Rep. Tom Price (R., Ga.), nominated to serve as Health and Human Services secretary, will become an early focal point for debate over any repeal plan, given the congressman's years of working to replace the health law's mandates with tax credits for the purchase of insurance.

Senate Republicans as soon as Tuesday will start a legislative process that would allow them to repeal much of the law with a simple majority vote -- a political necessity, given that they hold 52 seats in the chamber, shy of the 60 needed to pass most legislation. The first step would be to introduce and start debate on a budget resolution for the 2017 fiscal year, setting up passage by next week.

The resolution would direct Senate committees to reconcile tax and spending legislation with the budget blueprint, but also carry the broader goal of dismantling the Affordable Care Act. The resulting package would have special procedural protections allowing passage by a simple majority

Other early battles will include Senate consideration of Sen. Jeff Sessions (R., Ala.) to be attorney general, the first confirmation hearing on the calendar, set for Jan. 10-11. Mr. Sessions has drawn scrutiny from the left over his civil-rights record. A spokesperson for Mr. Sessions didn't immediately respond to a request for comment.

Tentative hearings are also scheduled on Jan. 11 for Michigan philanthropist Betsy DeVos, nominated to be secretary of education, and on Jan. 12 for fast-food executive Andy Puzder, nominated to head the Labor Department. Both are lightning rods for Democratic criticism, though there is no sign that the minority party has the votes to stop the confirmations.

Further in the distance: an expected battle over whoever Mr. Trump selects to fill an open seat on the Supreme Court.

Democrats say they will fight Mr. Trump and his GOP partners on policy differences. Mr. Obama is scheduled to visit Capitol Hill on Wednesday to meet with Democrats from both chambers to discuss strategy on their most urgent goal -- defending the Affordable Care Act.

The coming fights aren't confined to domestic policy. Sen. John McCain (R., Ariz.), chairman of the Senate Armed Services Committee, has scheduled a hearing for Thursday on cybersecurity, which he plans to use to delve into the U.S. intelligence community's conclusion that Russia hacked the Democratic National Committee's email system in order to interfere in the 2016 elections. That hearing could amplify GOP concerns about Mr. Trump on foreign policy, which have grown as Mr. Trump has praised Russian President Vladimir Putin and cast doubt on the intelligence community's conclusion in the hacking matter.

Taking up another foreign policy debate, the House this week is expected to vote on a resolution disapproving of the Obama administration's decision to allow the United Nations Security Council to condemn Israel's expansion of Jewish settlements in Palestinian areas. The House vote will be an early sign of support for Mr. Trump, who urged that the U.S. veto the U.N. resolution.

Stocks and consumer confidence have rallied since Mr. Trump's elections, in part on expectations of tax cuts and a regulatory rollback, and so Republicans are under pressure to follow through.

To reduce the regulatory burden on business, the House this week plans a vote on a bill known as the REINS Act, which would empower Congress to approve major new regulations written by federal agencies. The House also plans to vote on a measure to allow Congress to repeal a block of existing regulations at one time.

Neither measure is expected to pass given procedural hurdles in the Senate.

Congress could also use its power under the 1996 Congressional Review Act to repeal newer regulations on a simple majority vote, instead of requiring the filibuster-proof majority that is typical in the Senate. Once Mr. Trump is inaugurated, Republicans could use the law to repeal rules made since 2016, according to a recent estimate by the Congressional Research Service.

A top target is a regulation that expanded the number of workers subject to overtime-pay rules. Mr. Obama blocked five such attempts to repeal key elements of his regulatory agenda.

A rewrite of the tax code is likely to be more of a slog than a sprint. Republicans want to make the farthest-reaching tax code changes since 1986, lowering marginal rates on individuals and businesses and repealing the estate tax. They'll aim to use a legislative strategy that relies only on GOP votes, but it will require Republicans to unify around a single plan and fight past any interest groups that feel threatened.

Key differences are already evident. House and Senate Republicans say they're aiming for a plan that doesn't add to the deficit, after counting revenue from faster economic growth. Mr. Trump, however, has proposed a tax cut that even his campaign's optimistic projections say doesn't pay for itself.

To fill the budget hole caused by rate cuts, the House plan relies on imposing the U.S. corporate tax on imports and exempting exports. That so-called border adjustment would improve incentives for U.S. manufacturing and limit the benefits companies can get from shifting their addresses and jobs abroad. But retailers, refiners and other importers are pushing back and warning of higher consumer prices. Senate Republicans haven't warmed to that plan and Mr. Trump hasn't embraced it either.

House Republicans haven't released any draft legislative language or a schedule for a tax measure, but they want to move quickly.

Republicans also will have to respond to Mr. Trump's promises to build a wall along the border with Mexico -- and decide how literally they must take those promises in order to satisfy his powerful base.

The party wants to move quickly in order to fulfill the image Mr. Trump has painted of a government that can produce good jobs and wages with the right leadership.

History shows that unforeseen events can force Congress to rip up the agenda. In 2001, Mr. Bush had only just completed his first tax cuts when terrorists struck New York and Washington on Sept. 11. Within days, the Senate voted unanimously, and the House voted with only one "no" to authorize the use of military force to combat al Qaeda. The decision underpins interventions in Iraq today to stamp out Islamic State and drone strikes in nations such as Yemen and Pakistan. By October, Congress had passed the Patriot Act, which authorized the government to collect Americans' phone records.