The very word "operation" -- which has largely been banned by McChrystal's staff -- scares many residents who imagine a dramatic, airborne invasion of Kandahar City. At the same time, some residents fear the opposite: that a rhetorical emphasis on police and governance means no military effort to defeat the Taliban.
Others simply have lost faith in the United States and the Afghan government, who have failed to realize so many Afghan hopes after eight and a half years of war.
"If President Karzai's statements were put into practice, then we would be happy," said Haji Bacha AKhundzada, who is from Kandahar City. "Every time he comes here, he always says nice things. But we never see things actually getting done."
"Adding foreign forces and more bombardments won't create peace," said Toor Jan, who is from the Arghistan district east of Kandahar City. "Russians also launched a lot of bombardments. They killed many people, and they lost in the end."
American officials acknowledge the difficulty of convincing Kandaharis to support a massive influx of foreign troops when past campaigns have failed to deliver. American and Canadian troops have cleared much of Kandahar province in dozens of operations over the last eight years but never had enough forces to hold the areas and keep out insurgents.
The 2010 surge -- at the cost of $30 billion a year -- is designed to change that equation.
"What they have seen in the past is a lack of capacity on the part of the government and a lack of numbers on the coalition forces to achieve lasting security," McChrystal said, referring to Kandahar leaders. "They are naturally skeptical. And so I think we, together with the Afghan partners, have got to show that we can do it, and we can make it stick."
Still, last week McChrystal acknowledged that it was taking longer to gain the support of local elders than he had anticipated. American officials have delayed some of the most aggressive clearing and holding operations around the city until the fall -- partially due to a lack of support and partially due to a delay in Afghan Army forces' readiness.
Both American and Afghan officials acknowledge that support for the campaign is tempered by anxiety -- of possible civilian casualties, of Taliban retribution and of a spike in violence. They hope that, despite the likely toll the campaign will take on Kandaharis, the battle will be a decisive one for all of Afghanistan.
"This operation requires sacrifice," Karzai said. "And without sacrifice, you cannot restore peace to Kandahar."