Barack Obama

In the deal, Mr. Obama agreed to limit tax increases to higher income brackets than he originally proposed, and got less revenue than he was seeking. But the White House called the vote a landmark, representing the first time in two decades income tax rates had been increased for anyone.

The bill was expected to be signed quickly by Mr. Obama, who won re-election on a promise to increase taxes on the wealthy.

In the opening rounds of the showdown, Mr. Obama took a markedly tougher tone than he did during the failed budget talks held in the summer of 2011, when Republicans were threatening to let the country default by refusing to raise the federal debt ceiling. The president insisted in repeated public appearances that tax rates on the wealthy would have to rise, and ruled out any negotiations over raising the debt limit, which the Treasury said it would reach in early 2013, saying he was not going to “play that game.’'

2009-2010: Wins and Losses

In his first two years as president, Mr. Obama won passage of a number of sweeping pieces of legislation, notably a health care bill that promised to eventually provide near-universal coverage, a goal that had eluded Democratic presidents for 75 years. It passed in March 2010 after months of maneuvering to avoid a Republican filibuster in the Senate. After that, it had to survive a challenge in the courts: in June 2012, the Supreme Court upheld the law by a 5 to 4 margin, although it did limit the act’s planned expansion of Medicaid.

Other big victories included the $787 billion stimulus bill, passed in February 2009, meant to shore up a cratering economy, and a financial regulatory reform measure, passed in July 2010, meant to reduce the odds of another Wall Street meltdown.

But Senate Republicans blocked many other items on the president’s agenda, most notably a “cap and trade’’ energy bill, meant to reduce the growth of carbon emissions.  Mr. Obama’s popularity fell steadily into 2010 — from 70 percent to under 50 percent — as unemployment stayed stubbornly high, and conservative anger rose over the health care bill and a steeply rising deficit.

2010: ‘Shellacking’ in Midterm Elections; Some Victories

In November 2010, Republicans rolled to their greatest midterm gains in 80 years, recapturing the House of Representatives and cutting the Democrats’ majority in the Senate. After what Mr. Obama termed a “shellacking,’' he pronounced himself ready to cooperate with Republicans.

In the lame duck Congressional session that followed, Mr. Obama struck a compromise with Republican leaders on extending the Bush-era tax cuts for top earners, in return for a one-year cut in payroll taxes and an extension of unemployment benefits.

To the surprise of many, Mr. Obama and Congressional Democrats then rolled up a string of victories in the session’s closing days, including the repeal of the military’s “don’t ask, don’t tell" ban on gays serving openly, the ratification of the New Start treaty with Russia and the approval of a $4.2 billion fund for first responders made ill by the aftermath of the Sept. 11 attacks.

2011: Bin Laden Dies; Iraq War Ends; Debt Battle Rages

On May 1, in perhaps one of Mr. Obama’s greatest accomplishments while in office, he announced on television that American special forces had killed Osama bin Laden in a nighttime raid deep inside Pakistan. “Justice has been done,’' he said.

In June, Mr. Obama declared that the United States had largely achieved its goals in Afghanistan, setting in motion plans to withdraw 10,000 troops by the end of the year and complete withdrawal of troops by 2014. In mid-December, the American military formally ended its mission in Iraq.

On the domestic front, Mr. Obama was involved in a number of fiscal battles. After a new Congress convened in January 2011, the debate in Washington swiftly came to be dominated by the House Republicans. Spurred by a bloc of 87 largely conservative freshmen, they brought the federal government to the brink of a shutdown in April before Mr. Obama and Speaker John A. Boehner struck a deal to cut $38 billion out of the last six months of the 2011 fiscal year budget.

Mr. Boehner and his troops then focused on using the issue of increasing the government’s debt ceiling as a lever for forcing even deeper reductions. Mr. Obama responded by offering a “grand bargain’’ of $4 trillion in deficit reduction, including cuts to core Democratic programs like Social Security, Medicare and Medicaid, but conservatives in the House balked at the $1 billion in new revenues in the proposal.

In July, hours before a Treasury Department deadline for avoiding a possible default, Mr. Obama and Republican leaders struck a deal that would raise the ceiling through 2013 in return for at least $2.4 trillion in deficit reduction. The deal was criticized on all sides, and Mr. Obama saw his poll ratings sink to new lows, though not by as much as Mr. Boehner, Republicans and Congress in general. And the failure of the bipartisan Congressional commission, or “super committee,” to agree on a second round of deficit reduction did nothing to burnish reputations on either side of the aisle.

In the wake of the stalemate, and with the rise of the Occupy Wall Street movement, Mr. Obama began taking a more assertive tone. While Republicans blocked almost all of the $447 billion jobs bill he put forward in September and refused to consider his proposals to raise taxes on some wealthy households, they found themselves on the defensive over his call to extend the payroll tax cut agreed to in 2010. In late December, they agreed to extend the tax cut temporarily. Early the next year, it was extended for all of 2012.

2012: An Uphill Re-Election Bid; Health Care Law Upheld

On the domestic front, Mr. Obama declared for the first time in May that he supported same-sex marriage, putting the moral power of his presidency behind a social issue that has continued to divide the country.

In June, Mr. Obama’s controversial 2010 health care bill was upheld by the Supreme Court by a 5 to 4 margin, although it did limit the act’s planned expansion of Medicaid.

As for foreign policy, concerns about Iran’s nuclear program escalated with the publication of a report by United Nations weapons inspectors, which claimed there was credible evidence that Iran was developing nuclear weapons. The Obama administration and its European allies responded by imposing sweeping new sanctions meant to cut Iran off from the global oil market and isolate its central bank.

In 2012, Mr. Obama was also eager to bring to a close the second of two grinding wars his administration inherited from the Bush administration. In February, Defense Secretary Leon E. Panetta said that American forces would step back from a combat role in Afghanistan as early as mid-2013. In May, one year after the death of bin Laden, Mr. Obama made a surprise trip to Afghanistan where he met with President Hamid Karzai to sign a strategic partnership agreement that pledged American support for Afghanistan for 10 years.

In the ongoing conflict in Syria against the government of President Bashar al-Assad, the United Nations and many world leaders, including Mr. Obama, condemned Mr. Assad. But the president has remained keenly aware of larger forces at play — namely, Iran and Russia — and of the dangers of intervening in another Arab country.

Four Years Later, Scarred But Still Confident

Mr. Obama is a president who has yet to realize the lofty expectations that propelled him from obscurity to the Oval Office, whose idealism or naïveté or hubris has been tempered by four years in the fires. Long after the messiah jokes vanished, the oh-so-mortal Barack Hussein Obama must make the case that while progress is slow, he will be taking America to a better place — and that he will be a better president over the next four years.

Now on his third chief of staff, he describes his change in management in sports terms, no longer picking the best overall athlete but whoever best fits the particular job. Burned by failed Roosevelt Room summits with Republican leaders and faced with implacable resistance, he has abandoned the inside game to barnstorm the country pressuring lawmakers. Once a virtual prime minister tethered to Congress, he now advances immigration, environmental and education initiatives through executive authority.

In the privacy of the West Wing, of course, there are moments when he feels discouraged by what he has not accomplished or unappreciated for what he has. But those close to him say he takes the long view, understands things will not change as quickly as he likes, and retains his famed never-too-high, never-too-low reserve.

Mr. Obama sees himself as a rational thinker and came to office with what might be called the Reasonable Person Theory of Government. If he could simply sit down and talk with other political actors, whether they be Republicans from the House or mullahs from Tehran, he seemed certain he could work something out. His faith in his own powers of persuasion was deep.

But politics is often not rational, at least not as Mr. Obama defined it. The Iranians have proved immune to Mr. Obama’s charm, as have the North Koreans, the Taliban and Vladimir V. Putin. So have the Republicans and, for that matter, even some Democrats.

After a year of failed Middle East peacemaking, he conceded being too confident that he could cajole Israelis and Palestinians into resolving age-old disputes. “We overestimated our ability to persuade them to do so when their politics ran contrary to that,” he concluded at the time.

He keeps a list and argues that he has fulfilled most of his core promises. He pulled the country back from the economic abyss, rescued the auto industry, killed the world’s top terrorist, withdrew troops from Iraq, imposed regulations on Wall Street, put two liberal justices on the Supreme Court, signed a nuclear treaty with Russia and cut taxes for the middle class.

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