Karzai has been on the ground for almost a month conducting this dangerous mission, reports CBS News Correspondent Randall Pinkston.
"We all know if he is captured we know that they will kill him. That's for sure," says Karzai's younger brother Ahmed.
"I just spoke to him and he sounds very good. They are moving from one district to another, not worried about the Taliban. They are moving freely. We have enough forces there now."
Asked if this is the beginning of a challenge on the ground, Ahmed replied, "That's why my brother is inside there. That's a challenge to the Taliban, that's the beginning and I believe that will grow."
The Taliban claim Karzai's group was attacked last week and driven into the mountains, forcing a U. S. rescue a claim the Karzai family denies.
This weekend Defense Secretary Rumsfeld said U.S. planes did drop food and ammunition to Karzai, but there's no indication of any other U.S. support.
Hamid Karzai has many reasons to oppose the Taliban, and to hate Osama bin Laden.
"Osama bin Laden has not only killed Americans we hate what he did to Americans but that is not the fight we have with him. We have our own with him," Hamid said in September.
The Taliban agents of bin Laden killed his father.
He was murdered in a quiet Quetta neighborhood in 1999. The family had lived in exile in Quetta since the Soviet occupation of Afghanistan. The elder Karzai's murder not only robbed the family of a father, it also removed a catalyst for opposition to the Taliban.
Now, Hamid continues his father's legacy by challenging the Taliban on the ground. But the difficulty may be in persuading previously hostile tribes to bury their grievances.
Cobbling together an anti-Taliban opposition among the Pashtun peoples of the south - the ethnic group that dominates the Taliban movement - has been an elusive goal in the campaign against the militia, which has ruled Afghanistan for the past five years.
Karzai is a Pashtun, the country's largest ethnic group, and head of the large Popalzai clan, which has been linked to the Afghan dynasty that existed from the mid-18th century until King Mohammad Zaher Shah was deposed in 1973.
Urbane and fluent in English, Karzai is equally comfortable in a suit and tie discussing international politics or sitting cross-legged on a carpet, sipping tea with his fellow tribesmen.
If the Taliban are ousted from power, Karzai is seen as someone who could play a key role in a future Afghan government. He has a large natural following among his tribesmen and could encourage other Pashtuns to defect from the Taliban.
As a political moderate, Karzai is also seen as someone who could work with other factions, including the northern alliance, the opposition calition battling the Taliban.
Karzai has called for the former Afghan king, now 87 and living in Rome for more than a quarter century, to return to Afghanistan and serve as a symbolic leader of a broad-based government that would include all major ethnic groups.
The United States and its allies have been reluctant to see the northern alliance take power alone in Afghanistan: it is made up of ethnic minorities, and when it leaders held power from 1992 to 1996, their factional fighting caused a blood bath that killed at least 50,000 people.
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