"There's a notion that if you behead the snake, another two crawl out of the swamp," said one Justice Department official. "This situation is the opposite: cut off the snake's head and the body shrivels up. The important thing is to get the man."
While US President George W. Bush is promising that "time is running out" for Afghanistan's Taleban Government to hand over bin Laden, senior officials at the FBI are trying to buy time.
"This is not a war that will be won by impatience," said a security services official.
If a poorly plotted military attack allowed the world's most wanted man to escape, but killed innocents, the result would be catastrophic, the official said.
"This would just burnish his image and make the network even more determined. The worst thing would be a military operation that caused civilian casualties, let him escape and steeled the resolve of his operatives."
But the majority view, voiced most strongly by Mr Bush, is likely to be bolstered by news that bin Laden's terrorist army numbers no more than 2000.
Abdullah Anas, an Algerian Islamist who trained al Qaeda's military chief, Mohammed Atef, told a pan-Arab newspaper that the number of experienced fighters working for bin Laden had been grossly overestimated by Western Governments and reporters.
"Exaggerating the size of al Qaeda ... was to the liking of the American media."
But he believed it could take "many years" to destroy the group, especially as it had more than one mastermind.
Mohammed Atef is widely believed to be the brains behind the attacks of September 11. A US Government official said Atef and several of bin Laden's lieutenants orchestrated the suicide hijacking of four commercial airliners.
An Egyptian who used to work as a policeman and co-founded al Qaeda with bin Laden, Atef was instrumental in planning the 1998 bombings of the US embassies in Kenya and Tanzania.
Earlier this year his daughter married one of bin Laden's sons.
Map: Opposing forces in the war against terror
Afghanistan facts and links
Full coverage: Terror in America