Zardari travelled to Washington to attend a memorial service for the late Ambassador Richard Holbrooke, who died while serving as Mr. Obama's senior envoy to the Afghanistan-Pakistan region.
Months of disagreement between the two countries over the pace of Pakistan's effort to target hardcore Islamic militants on its side of the Pakistan-Afghanistan border have become a significant irritant in U.S.-Pakistan relations.
Most notably, Pakistan has refused to launch a major offensive against militants in the country's restive North Waziristan region, along the Afghan border, citing reasons related to its domestic security interests.
"A campaign in North Waziristan would be suicidal for Pakistan," one Pakistani security official tells CBS News on condition of anonymity. "There would be bloody reprisals in the shape of terrorist attacks targeting our main cities."
For the U.S., however, a North Waziristan offensive would represent a strong symbol of the Pakistani government's commitment to fighting extremists on its own soil - a clear message to the West, and its own citizens, that even senior Islamic hardliners with ties to the country's security services won't be tolerated.
U.S. officials have long pointed to North Waziristan as a haven for militants to regroup and train and then launch routine attacks across the border into Afghanistan, usually aimed at Western and Afghan forces.
Though Zardari is Pakistan's head of state, he does not wield more than token control over the country's powerful army, which has ruled Pakistan for more than half its existence as an independent state, and remains the key arbiter on matters related to security policy.
Equally alarming for the U.S. are recent signs that the resolve of Zardari and his ruling Pakistan People's Party (PPP) to confront Islamic extremists in the country's mainstream politics could be faltering. There are also concerns in the West that the government has failed to undertake vital economic reforms, considered necessary for overall stability.
Events leading up to and following the January 4 assassination of Salman Taseer, the influential governor of Pakistan's largest Punjab province and a personal friend of Zardari's, have exposed the government to criticism over its weakening stance.
Taseer was killed by one of his personal bodyguards who said later he was seeking revenge for the politician's criticism of Pakistan's controversial Islamic blasphemy laws. Human rights groups complain the blasphemy laws in their present form are vague and have at times been used to target people on flimsy evidence.
The case of Asiya Bibi, a Christian woman charged with blasphemy and sentenced to death in Pakistan, has divided the nation.
"It is important for people to stand up and be counted. Otherwise, this will unfortunately become an increasingly difficult situation for personal freedoms," the late Taseer told CBS News in an interview last year.
Taseer's public defense of Bibi enraged hardcore Islamists who sought his dismissal from the governor's seat. Before and after Taseer's death, Zardari's government has said repeatedly it has no intention to change or amend the blasphemy laws. But critics warn that by taking this position, the ruling political structure has only yielded further to pressure from radical elements of society.
"I think this debate is not just about blasphemy itself. It is more about the way the application of the law has to be discussed, debated and the controversy has to be resolved," Saeed Jamal, a lawyer who visited the site of Taseer's assassination, told CBS News. "The government has not even managed to move that much to consider how the law is applied in Pakistan."
On the economic side, Pakistan's government is wracked in debt and continues to function thanks to massive infusions of foreign aid money - including a promised $7.5 billion infusion from U.S. tax payers over the next five years.
The U.S. remains concerned over the continued failure to broaden the tax net in a country where less than one percent of the population of 180 million pays any income tax. Yet, PPP leaders rebut the criticism by arguing that painful economic reforms at this time, when internal politics remains uncertain and security conditions are challenging, risks creating a powerful anti-government backlash on streets across Pakistan.