WASHINGTON — A deeply divided Congress is being called back into session this week to deal with a host of urgent issues, setting the stage for a showdown between a wounded Democratic Party and newly empowered Republicans in which both sides know that gridlock could substantially raise taxes on most Americans.

The recalled Congress, including some 60 members ousted in 2010 elections, and with Nancy Pelosi still presiding as House speaker, must decide whether to extend Bush-era tax cuts that expire at year’s end. A Massachusetts family making the median income of about $81,000 would pay an extra $1,800 in taxes next year unless Congress takes action, according to the nonpartisan Tax Foundation research group.

The lame-duck Congress must also decide whether to delay the enactment of a 23-percent pay cut for doctors who treat Medicare patients, and whether about 2 million jobless Americans will lose their unemployment benefits during the holidays.

To add to the degree of difficulty, dealing with these problems could add to the federal deficit at a time when post-election sen timent is to try to balance the budget and there’s little indication the Republican election landslide has eased partisanship on Capitol Hill.

“There are a lot of issues the Democrats would like to deal with before Republicans take over the House,’’ said Julian Zelizer, a Princeton University professor of history and public affairs. But “Republicans will be more powerful within a few months, so it’s not clear why they would give in to the Democrats at this point and do anything that would get them in trouble with their base.’’

There could be a political price to pay by all parties, however, if gridlock over the next several weeks results in higher taxes for the middle class. There is broad agreement in Congress to extend Bush-era tax cuts for middle-class families, but that agreement could be jeopardized in a standoff over what to do with taxes on higher income households. President Obama wants the tax cuts to expire on family income above $250,000; Republicans insist on keeping the current rates for all income.

“Would Republicans not agree to extend the tax cuts for middle and lower incomes as a way to get everybody’s taxes extended, including the upper incomes?’’ said Gerald Prante, an economist at The Tax Foundation. “And vice versa: Would Democrats hold hostage those middle-income tax cuts in order to prevent the top from getting a cut?’’

For President Obama, who said after the election that he and his party took a “shellacking,’’ the lame-duck session is his first opportunity to reboot his chilly relationship with congressional Republicans who have opposed nearly his entire agenda. The president has invited congressional leaders from both parties to the White House on Thursday to discuss the tax impasse, and has signaled that he is willing to compromise on tax cuts for higher incomes.

Republicans so far are standing firm. “Extending all of the current tax rates, and making them permanent, will reduce the uncertainty in America, and help small businesses to create jobs again,’’ Representative John Boehner, the Ohio Republican expected to become the next House speaker, told reporters last week.

Some Democrats see the expiring tax cuts on upper incomes as an opening to attack the deficit without raising the ire of the middle class. “There is an opportunity to begin to deal with the difficult issue of the deficit, since extending the cut for the wealthiest Americans would require on the order of $600 billion to $700 billion of borrowing over the next 10 years,’’ said Senator Jack Reed, Democrat of Rhode Island, in an interview.

The short session is the last gasp for the Democratic majority in the House before it must surrender control to the Republicans when the new Congress is sworn in this January. The GOP also gained six US Senate seats, though the Democrats, who will control 53 seats next year, will maintain a majority. A question hovering over the lame-duck session is whether Democrats will return to Capitol Hill undeterred, or cowed by their Election Day rebuke.

“The Republicans obviously are ascendant because of their numbers coming in,’’ said Representative Stephen Lynch, a South Boston Democrat reelected earlier this month. “Anything we as Democrats suggest right now is seen in the light of a lame-duck session. Anything we propose doing will be criticized as, ‘Oh, you’re trying to subvert the mandate in the most recent election.’ There’s some strength to that argument.’’

Representative Connie Mack, a Florida Republican, said in an interview that Democrats should heed the message of the midterm elections and extend the tax cuts and embrace more conservative ideas.

“They don’t seem to understand what the American people are telling them, and that is, they don’t want more government, they don’t want more taxes, they don’t want more spending,’’ Mack said. “I think a lot of Democrats will start to hear that message and will support ideas like extending all of the tax cuts instead of playing games with some of the tax cuts.

“I also think there’s a really good chance that you’ll have a strong core of very liberal Democrats who will support Pelosi but they will become a minority even in their own party.’’

The tax issue is just one of several deadline decisions facing Congress in the lame-duck session. Unless the House and Senate take action, doctors will see the payments they receive for treating Medicare patients slashed by about 23 percent next month, said Dr. Alice Coombs, president of the Massachusetts Medical Society.

The cuts stem from a reimbursement formula in federal law, which doctors say is obsolete. Congress has repeatedly voted to delay cuts in Medicare payments. If the cuts are enacted, doctors might have to close their offices or drop Medicare patients, she said.

“Unfortunately, some doctors will have to make decisions based on their practice’s viability in order to stay afloat,’’ said Coombs.

Another key issue is unemployment benefits for people who have exhausted their normal 26 weeks of state-paid benefits.

The federal government has been paying to extend benefits for the long-term unemployed, up to a total of 99 weeks in some economically hard-hit areas, according to Judy Conti, federal advocacy coordinator for the National Employment Law Project. The extensions are set to expire at the end of November.

If the program is not reauthorized, 2 million people will lose benefits, including 52,000 from Massachusetts, she said. Reauthorizing the program for another year would cost $60 billion. It’s a sticky issue in the current political climate because the benefits have been paid by the government by emergency borrowing, which adds to the deficit.

On foreign policy, President Obama wants the Senate to confirm the new Strategic Arms Reduction Treaty, which Obama signed with Russian President Dmitry Medvedev. The agreement to cut nuclear arms needs 67 votes to be ratified. Several key Republicans have raised questions about language and have warned the president not to try to push it through the Senate too quickly.

Other items before the Congress this month include a food safety bill that has been stuck in the US Senate, and the so-called DREAM Act, a proposal to provide a path to citizenship for certain young illegal immigrants who attend college or serve in the military.

Senate Majority Leader Harry Reid, a Nevada Democrat who won reelection over a furious Tea Party-fueled challenge in the midterm election, pledged during his campaign to bring the DREAM Act forward in the lame-duck session.

Many conservatives staunchly oppose anything resembling “amnesty’’ for people who came to the US illegally. A number of legislative compromises over the past five years have failed.

Matt Viser of the Globe Washington Bureau contributed to this report.