Obama's goal is to get through that trifecta and still have the political capital left for the things he'd rather focus on: reducing gun violence, overhauling immigration policy, revamping tax laws, addressing climate change and more.
With Republicans in Congress approaching the new year with very different goals, "it's a formula for deadlock and difficulty for the president," says James Thurber, director of the Center for Congressional and Presidential Studies at American University. "I don't think this president has even a month of political capital."
The president also will have to devote significant energy simply to safeguarding the achievements of his first term, by keeping the economic recovery alive, making sure his health care law is properly put in place in the face of persisting objections from businesses and individuals, and ensuring new financial regulations have teeth.
International worries, including the civil war in Syria, Iran's nuclear intentions and instability in Mali could complicate the president's Term Two game plan as well.
"Things are stacked up," Obama senior adviser David Plouffe acknowledged Sunday on ABC's "This Week."
Plouffe argued that the president's big agenda gives him "the sort of focus and energy you need. And I think his intention is to run through the tape all the way."
Obama can take heart from any number of things he has going for him. He has a can-do attitude, growing public support for action on some of his chosen issues and better approval ratings.
Democrats gained seats in both houses of Congress in the November election and Republican poll numbers are weak. With the war in Iraq over and U.S. military involvement in Afghanistan winding down, he has more time to focus on domestic priorities. He also doesn't have to worry as much about ruffling feathers because he doesn't have to run for re-election again.
"People shouldn't underestimate how much we can get done," the president said in a pre-election interview for Rolling Stone.
Obama also understands the underwhelming track record of second-term presidents and the dangers of over-reaching. "We are very cautious about that," he said.
The president hopes to strike a hopeful theme in his second inaugural address on Monday. But he knows that partisanship only worsened during his first term.
"The optimism of his 2008 campaign about bridging divides has not been realized at the end of the first term, and there's very little prospect that it's going to be coming into a second term, so the language has to be careful," says Kathleen Hall Jamieson, director of the University of Pennsylvania's Annenberg Public Policy Center.
Immigration offers Obama perhaps his best chance at a significant second-term achievement. The 2012 elections, in which Obama drew lopsided support from Hispanics, gave Republicans a wake-up call on their need to pay more attention to Latinos, so the GOP is more inclined to work with the president there than on other issues.
The problem is incredibly complex, though, and past efforts at comprehensive change have failed. The question of how to deal with the estimated 11 million people already illegally in the U.S. is the big sticking point.
On gun control, an issue where Obama moved quickly after the Connecticut elementary school shooting, the president faces longer odds in Congress.
The president knows that.
He promised to "put everything I've got" into the effort. But he also put people on notice that the effort will only succeed "if the American people demand it." That reflects his growing recognition that the only way to make an end-run around Washington gridlock is by leveraging public will.
The polling on guns, then, may offer clues to what elements of the president's package have the best chances of enactment.
More than 80 percent of adults back setting a federal standard for background checks on people buying guns at gun shows. By comparison, 55 percent favor a nationwide ban on military-style, rapid-fire guns. That prohibition appears to have few chances of passing Congress.
Obama is sure to tangle with Congress again over spending and taxes as legislators grapple with the next three installments in the continuing "fiscal cliff" drama.
And that will roll right into the broader struggle over tax changes and setting the country on a more sustainable fiscal path, where Obama will have to seek consensus with a Republican-dominated House in which conservatives hold sway and moderates are no longer an endangered species but truly gone, Thurber says.
The president hopes for a "grand bargain" that reduces the deficit over the long term, but the trick is to achieve that goal while safeguarding Medicare, Medicaid and Social Security for future generations. A package that does both would go a long way toward expanding the legacy Obama began to build in his first term with action on health care and rescuing the economy.
The president enters his second with a new team taking shape and new strategies to deploy, but also more aware of the challenges inherent in the current atmosphere of polarization.
He describes himself as a "happy warrior" ready to do battle anew.
But Calvin Jillson, a political scientist at Southern Methodist University, says Obama is still "as much an academic as a politician."
"What I don't think he's done is learn how to wield the power of the presidency in ways that former presidents have," says Jillson. "It's possible that Washington is just too different, and that what was possible for FDR or Lyndon Johnson is simply not possible today, even in light of large Democratic majorities in 2009-2010. Maybe Washington is just a different place."