WASHINGTON — Congress returns Tuesday to a crowded agenda of unfinished business overshadowed by the urgent need for President Barack Obama and lawmakers to avert the economic double hit of tax increases and automatic spending cuts.

One week after the elections — and seven weeks after they last gathered in Washington, Republicans and Democrats face a daunting task in a lame-duck session that Capitol Hill fears could last until the final hours of Dec. 31. But even before serious budget negotiations can begin, lawmakers will tackle leftover legislation on trade with Russia, military budgets and aiding farmers still reeling from the summer's drought.

The first days back will be a mix of old and new — choosing down-ballot leaders 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.

While the nation's voters endorsed the status quo of divided government — a Democratic president and Senate, a Republican House — Obama cruised to re-election and his emboldened party gained seats in both the House and Senate. In the new political order, Democrats will hold a 55-45 edge in the Senate if independent Angus King of Maine caucuses with them as expected. Republicans' advantage in the House narrows and likely will stand at 233-201.

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The question over the next seven weeks is whether Obama and Congress can agree now or later on how to slash $1.2 trillion from the deficit, raise revenues with possible changes in the tax code and address the entitlement programs of Social Security and Medicare.

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