WASHINGTON, Nov 3 – Whipsawed by events and facing another midterm electoral defeat, President Obama has directed his team to forge a policy agenda to regain momentum for his final two years in office even as some advisers urge that he rethink the way he governs. Without waiting for results from elections on Tuesday that few in the White House expect to go well for Mr. Obama, top aides have met for weeks to plot the final quarter of his presidency.

Anticipating a less friendly Congress, they are mapping possible compromises with Republicans to expand trade, overhaul taxes and build roads and bridges. For a president who has lost public support and largely failed to move his agenda on Capitol Hill since winning re-election two years ago, there may be little hope for significant progress if Republicans capture the Senate and add to their House majority.

But if Republicans are fully in charge of Congress rather than mainly an opposition party, both sides may have an incentive to strike deals, at least during a short window before the 2016 presidential campaign consumes Washington. With or without partners on Capitol Hill, Mr. Obama will continue to exercise his executive authority to advance Democratic policies on climate change, immigration, energy, gay rights and economic issues, aides said.

The president, in fact, may announce quickly after the election a unilateral overhaul of immigration rules to make it easier for millions who are in the country illegally to stay. And, of course, many presidents in their last years turn more to foreign policy, where they have a freer hand to set direction. “There’s still lots of time to get things done,” said Senator Bob Casey, a Pennsylvania Democrat described by some White House aides as one of the president’s closest allies in Congress.

“I’m actually optimistic about what he can accomplish in these next two years.” But as he sorts through the results this week, and in weeks to come if some Senate races go to runoff elections, Mr. Obama will also confront the question of whether he needs to change the way he operates. Even some of his strongest supporters are quietly recommending changes in his staff and a more open decision-making process.

Among advisers inside and outside the White House, there is a growing sense that Mr. Obama has closed himself off within a shrinking circle of aides. Some advisers who had been influential said they were no longer consulted as much. They worry that Denis McDonough, the White House chief of staff, has taken on too much himself.

“The circle is small,” said a former senior administration official who did not want to be identified discussing former colleagues. “Particularly if the Republicans take over, I would like him to expand that group and bring in some people from the outside.” A commonly cited model is President Ronald Reagan’s decision to enlist former Senator Howard Baker and a team including Kenneth Duberstein.

“I just think you’ve got to take that risk and go outside your comfort zone of recycled Obama staff people,” the former Obama official said. Some turnover is likely. John D. Podesta, the president’s counselor, has resisted requests to stay and is likely to leave after the State of the Union address to head Hillary Rodham Clinton’s presidential campaign.

Longtime Obama aides exhausted after eight years of campaigning and governing, including confidants like Dan Pfeiffer and Benjamin J. Rhodes, have thought about whether to move on. As the president’s advisers map out the next two years, they have focused on three broad categories: agenda items he can advance without Congress, legislation that might emerge from a newfound spirit of compromise with Republicans, and issues that Mr. Obama can promote even without hope of passage as a way to frame the party’s core beliefs heading into 2016.

Beyond immigration, aides said, Mr. Obama is determined to use his power to push for more environmental rules to curb climate change, and they said new Democratic governors could give the president a chance to expand the reach of his health care program in states where Republican governors had resisted. But Mr. Obama has to weigh the consequences of provoking Republicans by using his power to bypass them if he wants to find compromises, too.

“The world is going to look one of several ways on Wednesday morning,” said a senior White House official, who described strategy on the condition of anonymity. “The challenge to date has been the Republican unwillingness to compromise. Will that change after Tuesday’s elections? It’s too early to say. No one is naïvely thinking that the dynamics are going to change easily.”

David Axelrod, a former adviser to Mr. Obama, said the president should make a fresh effort to work with the new Congress despite deep frustrations that led him to bypass legislators this year. “I really think he has to feel out what there’s a willingness to do,” he said. “What he can’t do and won’t do is put his feet up on the desk and cross days off the calendar.”

Joel P. Johnson, who was Bill Clinton’s counselor late in his presidency, said Mr. Obama should test Republican intentions soon after the new Congress takes office. “Make it clear there is a negotiating table awaiting, and don’t shut down the possibility that there could be a dialogue that results in something that’s progress,” he said.

In some ways, a change in the Senate majority may not make that big a difference. Other than presidential nominations, which can be passed with a simple majority, most significant legislation must still muster 60 votes, which neither party will have, to overcome a filibuster. One Democrat close to the White House said the election was just “the difference between 96 percent gridlock and 100 percent gridlock.”

And there is considerable scar tissue. Democrats assume that Republicans may be beholden to their more conservative elements. “That’s the $64,000 question,” Senator Charles E. Schumer, Democrat of New York, said. “After the election, will the Tea Party hard right or will mainstream conservatives call the shots? If it’s mainstream conservatives, rather than the Tea Party, then I think there are some things that are possible.”

For Mr. Obama, the question may be whether he is liberated from deferring to Senator Harry Reid, the Democratic majority leader, if the party is in the minority. Some Democrats said Mr. Obama had more interest in forging deals than Mr. Reid and could take the lead in brokering agreements. Others, though, said Mr. Reid may be so determined to recapture the Senate in 2016, he will resist deals that give vulnerable Republicans like Senator Kelly Ayotte of New Hampshire any successes to run on.

Republicans said the onus would be on Mr. Obama, faulting him for being unwilling to accommodate the opposition. Representative Tom Cole, Republican of Oklahoma, said Mr. Obama must choose whether to work across the aisle or define his legacy by opposing an emboldened Republican Party. He added that his party faced a similar choice.

“You are going to have to have both parties give up more than they’d like to get less than they want,” Mr. Cole said. “It will be as much a test for the Republicans as the Democrats.” Republicans noted that the House had passed dozens of bills bottled up by Senate Democrats and suggested that compromise on some could be a way forward.

“If they take a more realistic approach to life and not this designed-to-fail thing, then we can get a lot of stuff done,” said Don Stewart, deputy chief of staff for Senator Mitch McConnell of Kentucky, the Republican leader. “If you start with those, that would keep us busy for a year.” White House officials see potential for legislation on cybersecurity, energy, sentencing guidelines and surveillance.

But the three areas most cited are trade, corporate taxes and infrastructure. Democrats like Mr. Reid have resisted giving Mr. Obama trade negotiating authority, so a Republican Senate may be better for the president on this issue. And yet, there are deep disagreements even in these areas. Mr. Obama, for instance, wants to rewrite the corporate tax code to bring down rates while closing loopholes.

Republicans want a broader overhaul, including personal income taxes, since small businesses pay taxes that way. Still, Representative Charlie Dent, Republican of Pennsylvania, expressed optimism. “I’m sure there are going to be other partisan fights, particularly if the president continues to overreach administratively,” he said. “That will create some friction. But those three issues are ripe for bipartisanship.”

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