Fresh from a bruising victory on health care and a nuclear arms deal with Russia, President Barack Obama turned to a third campaign promise – victory and an honourable exit from Afghanistan. That could prove tougher than any challenge overcome so far, and the president appears to know it.

Seldom does a US leader devote more than 24 hours flying to and from a war zone to spend only six hours on the ground. But the stakes are enormous.

Since taking office, Obama has nearly tripled the number of US forces committed to Afghanistan, which hasn’t known peace in at least three decades. After eight years of war, the US military says it now is blunting advances by Taliban militants, but Afghan President Hamid Karzai still has little power outside Kabul, the capital, and his government is riddled with corruption.

Al-Qaeda leader Osama bin Laden, key lieutenants and foot soldiers still hide across the mountainous border in Pakistan even though US drone strikes have killed dozens of the terrorist group responsible for the September 11 attacks on the United States. Al-Qaeda enjoyed sanctuary from Taliban militants who ruled Afghanistan, before they were driven out in the US-led invasion at the end of 2001.

Obama campaigned on a pledge to focus on the Afghan war, which he said – unlike the fight in Iraq – was critical to American security and being overlooked and poorly resourced by the Bush administration.

Despite the highly charged partisan atmosphere, where no Republican voted for the health-care legislation in either house of Congress, the president enjoys broad GOP support for his intensification of the Afghan war.

There appears, as well, growing support among the public for Obama’s Afghan policy.

The latest Associated Press-GfK poll at the beginning of March found that 57 per cent of those surveyed approved his handling of the war compared with 49 per cent two months earlier.

The Obama-Karzai meeting lasted about 30 minutes, and Obama told the Afghan leader he saw some progress since they last talked in video conference two weeks ago. They discussed good governance, merit-based appointments of Afghan officials and corruption. The administration has routinely chastised Karzai for failing to make progress on those issues.

National security adviser James Jones said after the meetings that Karzai “needs to be seized with how important that is”.

The long journey, Jones said, was “something that simply has to be done. We have to have the strategic rapport with President Karzai and his Cabinet to understand how we are going to succeed this year in reversing the momentum of the Taliban.”

Karzai spokesman Waheed Omar, however, said reports that Obama was in Kabul to order a recalcitrant Karzai to get his government in line were inaccurate.

“This was an extremely friendly discussion,” Omar said. “It was a discussion between partners.”

He said Obama pledged not to abandon Afghanistan.

“President Obama assured President Karzai and the Afghan people of America’s long-term commitment to Afghanistan,” Omar said.

Obama’s surprise visit underscores the political stakes for him. As he dispatched the most recent instalment of his 30,000-troop increase to Afghanistan, the president pledged to begin withdrawing US forces in July 2011, when his campaign for a second term would be well under way.

That will be a difficult pledge to keep if Karzai doesn’t intensify a corruption purge.

Karzai pledged after the fraud-marred August election to mop up the stain of corruption by making officials declare assets and giving the country’s anti-corruption watchdog more power.

The Afghan leader has tried with little success to tackle corruption in the past, and the non-governmental organisation Transparency International last year ranked Afghanistan 176th out of 180 countries. Its annual poll assessing perceptions of corruption among public officials and politicians found only Haiti, Iraq, Myanmar and Somalia ranking lower.

The face of the Karzai administration is still marked by two former warlords who serve as his vice-presidents. There also are supposed to be 25 members of his Cabinet, but since the August election parliament has approved only 14, claiming the other 11 nominees are either incompetent, corrupt or too weak to resist pressure from powerful people. He tried twice to get the full list ratified; after the second failure, he named the 11 acting ministers. It’s not clear how long they can serve.

Not clear, either, is how long Obama can sustain his winning streak with domestic and foreign policy. Republicans are predicting a major victory in November mid-term elections, forecasting that American voters are prepared for a wholesale rejection of congressional Democrats who voted for the health care law.

What’s more, some Senate Republicans are talking as if they may lead a fight against ratification of the new treaty with Russia. To go into force, the nuclear arms deal must win two-thirds backing, a mighty challenge in the blazing partisanship gripping the capital.