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Congress returns to work Tuesday with a laundry list of unfinished business, arguably none of it more pressing than trying to avert the economic double whammy of tax increases and huge federal spending cuts that would have an impact on all Americans.

The House and Senate would have to work quickly to reach deals to avoid one or both scenarios and keep America from going off the so-called “fiscal cliff,” considering the 112th Congress' session concludes Dec. 31.

Capitol Hill Republicans and Democrats were deadlocked on these issues long before the seven-week vacation that allowed all House members and roughly two dozen senators to campaign for re-election.

However, both sides have shown some signs of compromise on the nearly $1 trillion in automatic federal cuts – accepted in theory by both parties when Congress and President Obama could not agree on a more measured plan to reduce the federal deficit.

Since Election Day, House Speaker John Boehner and other Republicans have suggested that closing tax loopholes used by the country’s highest wage earners would be a way of raising revenue without increasing the top tax rates.

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However, Democrats have argued that although the lower Bush-era tax rates should be maintained for most Americans, they should allowed to expire for top earners, meaning a tax increase for the largest 2 percent of incomes.

The congressional lame duck session -- in which lawmakers who lost re-election still must participate – will also address such leftover legislation as trade with Russia, military budgets and aide for farmers still reeling from the summer's drought.

The first days back will be a mix of old and new – assigning leadership jobs in the Senate while the 12 new members, three Republicans, eight Democrats and one independent, are introduced to their colleagues.

The House will welcome some 70 new members, who will get a crash course on how Congress operates with a class on ethics Wednesday.

Voters last week voted for essentially the same government they had – a Democratic president and a Democratic-controlled Senate with a Republican-led House, though Democrats gained seats in both chambers.

They have a 55-45 majority in the Senate if Maine independent Angus King caucuses with them, as expected. The Republicans' advantage in the House narrows and likely will stand at 232-202.

Democrats were leading in the five undecided House races – in California, Florida, North Carolina and Utah.

On Monday ,the Associated Press called the House race in Arizona for former Democratic state Sen. Kyrsten Sinema. She defeated Republican Vernon Parker in the race to represent a new Phoenix-area congressional district.

Still, the question over the next seven weeks in Washington is whether Obama and Congress can agree now or later on how to slash $1.2 trillion from the deficit.

And they also have to figure out how to stop the across-the-board cuts to defense and domestic programs -- totaling $110 billion next year.

Obama is scheduled to meet Friday with congressional leaders at the White House. Democrats and Republicans recognize the urgency, but the demands remain unchanged.

"If our Republican counterparts can step forward with that revenue piece, we will be able to find a solution," Sen. Patty Murray, D-Wash., said Sunday on ABC's "This Week." `'We can't accept an unfair deal that piles on the middle class and tell them they have to support it. We have to make sure that the wealthiest Americans pay their fair share."

The GOP insisted Sunday that tax rate increases are a non-starter.

"There's a right way to do this and there's a wrong way to do it," Sen. Saxby Chambliss, R-Ga., said Sunday.

Boehner, R-Ohio, last week has signaled that a solution is imperative.

"2013 should be the year we begin to solve our debt through tax reform and entitlement reform," he told reporters.

Crucial in the House this week is passage of legislation that would end Cold War trade restrictions so that U.S. exporters can take advantage of the lowered tariffs and greater market access that accompany Russia's entry into the World Trade Organization. Russia officially joined the WTO in August and the United States is alone among more than 150 WTO members in not being able to enjoy the more open Russian market.

The Senate holds a procedural vote Tuesday on a bill that combines 19 measures favorable to outdoorsmen, allowing more hunting and fishing on federal lands, letting bow hunters cross federal land where hunting isn't allowed and encouraging federal land agencies to cooperate with state and local authorities to maintain shooting ranges.

A five-year farm bill passed by the Senate and by House committee last summer will either have to be extended into next year or passed in the remaining weeks of the session. The 2008 farm bill expired Sept. 30.

Legislation setting defense policy remains undone, and the House and Senate Armed Services committees were working informally in recent weeks on a bipartisan bill that both chambers could pass.

The House approved legislation months ago, but the Senate hasn't acted. The freestanding Senate bill has attracted more than 70 amendments and Majority Leader Harry Reid, D-Nev., is pressing for a time agreement that would limit amendments.

Republicans and Democrats will meet Wednesday morning in the Senate to decide on the leadership jobs, with Sen. John Cornyn, R-Texas, expected to move to the party’s No. 2 spot, replacing Sen. Jon Kyl, R-Ariz., who is retiring.

In the House, Reps. Cathy McMorris Rogers, R-Wash., and Rep. Tom Price, R-Ga., are vying for the No. 4 job.

The biggest question in the House ranks is whether Minority Leader Nancy Pelosi, D-Calif., remains in her leadership job.

The Associated Press contributed to this report.