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Jacquelyn Martin, Associated Press
President Barack Obama leaves the White House for Christmas in Hawaii on board Marine One, in Washington, on Friday, Dec. 23, 2011.

WASHINGTON — On a political high, President Barack Obama capped a bruising year by securing a tax cut for millions of Americans — an achievement that overshadowed Washington's deepening dysfunction and the slow progress of the economy on his watch.

The White House has ended a year with a political victory before. This time around the stakes are higher, and the president is by no means assured of carrying the momentum deep into an election year.

Addressing reporters before heading to Hawaii on Friday, Obama looked like a president in command of the stage again, for now. He left the capital after presiding over a two-month extension of a payroll tax cut — about $40 per paycheck for someone making $50,000 a year — that came when House Republicans caved on demands for a longer deal.

Yet on this issue, like many, enormous work remains for Obama after the new year, just when voters begin choosing a Republican nominee to try to oust him from his job.

Obama initially had pushed for a year-long extension of both the Social Security payroll tax cut and unemployment benefits. He got only two months on both because Congress could not agree on how to pay the bill for more without gutting their own political priorities — the same problem that awaits all sides in the weeks to come.

Although Obama calls a full-year extension a "formality," politically, it is not. So he pushed Congress to work "without drama, without delay" when they return from their own recess.

The whole scene was reminiscent of a year ago, when Obama took a self-described "shellacking" in the midterm elections but still ended up leaving for his yearly Hawaiian holiday on a high note.

In a news conference at the time, a jubilant Obama claimed a "season of progress" after stringing together legislative victories in a lame-duck congressional session, including the repeal of the military's ban on openly gay service members and approval of a new nuclear treaty with Russia.

But progress was short-lived. Obama returned to Washington in January to face a divided Congress and a Republican party prepared to push him to the brink.

This time, Obama left without taking questions from reporters, ensuring no disruption from the narrative all over Washington — a win for him, a capitulation for House Republicans. Had he engaged the press, Obama may well have been challenged about violence in Iraq since a U.S. troop withdrawal, or his own flip-flop over an oil pipeline included in the tax deal.

Obama may have won the messaging war this December, preventing higher taxes for 160 million Americans. But he gave up plenty to get a deal.

In securing the short-term extension, Obama caved on the controversial Keystone XL pipeline. The president had boldly said he would reject any effort to tie the payroll tax extension to the proposed Canada-to-Texas pipeline; he later gave in to GOP demands to make a decision on the project within 60 days.

Given that the House Republicans' backpedaling far overshadowed the president's compromises, GOP consultant John Feehery said Republican lawmakers are likely to come back to Washington in January even more motivated to take on the president.

"This is a temporary victory," Feehery said. "We're going to go back to the fight once again in a month and a half. This is one battle, not the whole war."

Obama's willingness to stand firm could help rally support among Democrats who have complained that the president too often seems to give in too much.

Obama's hard line at the end of the payroll tax cut talks sent an important message both to his supporters and Republicans, Democratic strategist Karen Finney said. She said both have misinterpreted Obama's prior compromises as a sign of weakness.

"In this instance it was certainly critical that the president not give any more ground," Finney said. "He showed that he does have a point at which he won't go farther."

The economy has been showing signs of coming around, too, which is vital to Obama's chances for a second term. But this is another area in which today's optimism can turn troubling at any time, with outside forces such as Europe's economic woes threatening to dampen the American recovery.

Each year, partisan debate and unfinished business have forced the president to delay departure for his cherished Christmas vacation in Hawaii. This December's stalemate threatened to derail the trip entirely, given that Obama himself pledged to stay in Washington until a deal to extend the cuts was reached.

Obama's original Dec. 17 departure date came and went.

It was only Friday, after the House and Senate finalized the deal, that the White House announced Obama's departure for later in the day.

The president has no public events planned during what is expected to be about a 10-day vacation. He typically spends his days in Hawaii playing golf or going to the beach with his family, though he makes occasional outings for dinner with friends.

The White House says the president's focus will be on spending time with his family. But there will be a small team of advisers traveling with Obama to brief him daily on domestic and international events — and to help him get ready for the work, and the battles, that wait in January.

Follow Julie Pace at http://twitter.com/jpaceDC