"What are his chances for survival?" asks Thomas Krajeski, who served as US ambassador to Yemen from 2004 to 2007.
"I'd give him about a fifty-fifty right now. And I don't think that's being generous. A lot of folks are inclined to give him less," he told an audience of foreign policy specialists in Washington.
Growing demonstrations in Sanaa, flaring secessionist sentiment in the country's south and a tribal rebellion in the north have all combined to shake Saleh, a crucial but difficult US ally in its struggle against Al-Qaeda.
A poor have-not of a state in a region famous for its oil and gas riches, Yemen has long been a source of great strategic anxiety for the United States.
Its long border with Saudi Arabia, its location at the southern entrance to the Red Sea, and its unruly tribal makeup have made it a prime target for Al-Qaeda, whose Yemeni affiliate is now seen as the group's most active.
Al-Qaeda in the Arabian Peninsula has been accused of the attempted bombing of a US airliner on Christmas Day in 2009, allegedly by a Nigerian trained in Yemen.
It is also believed to have been behind the nearly successful assassination of Saudi Arabia's deputy interior minister, Prince Mohammad bin Nayef.
The United States has sent special forces to train Yemeni counter-terrorism units, the army's special forces and the Coast Guard in hopes of containing the threat.
But the challenge to Saleh poses a dilemma for Washington, which supports political and economic reform but also wants to protect its counter-terrorism presence, experts say.
"My view is that this is the best partner we're going to have," said Gary Reid, a deputy assistant secretary of defense who oversees US special operations and an array of anti-terrorism programs.
"I would certainly hate to start over again in what we're trying to build."
US involvement in Yemen has depended entirely on Saleh, who has dominated the country since coming to power in a military coup in 1978. He became president of a reunified Yemen in 1990.
"For better or worse, he's it," said Krajeski. "Ali Abdullah Saleh is our main conduit to everything we are trying to do in Yemen."
Krajeski said he thinks Saleh will weather the latest challenge, as he has other periods of turbulence, citing his skills as a deal-maker.
"He knows how to make a deal, whether it is with us, whether it is with the tribes, whether it's with the southerners, where it's with Al-Qaeda. He'll deal with anybody," he said.
"So I'm not going to discount him. However, I do think the challenge that confronts Ali Abdullah Saleh may be too great for him right now," he said.
The ambassador, who currently serves as vice president of the National Defense University, said a tribal council currently meeting in Sanaa is likely to play a key role in determining his fate.
"If they make a deal among themselves, among the tribes in the north and other factors in Yemen, and that deal doesn't include Saleh, he's in trouble."
The appearance of a leading cleric, Abdul Majeed al-Zendani, at a huge protest in Sanaa on Tuesday was another bad sign. Zendani, who criticized Saleh, has been sanctioned by Washington as a "terrorism financier."
"Saleh has worked very hard to keep this guy in control. He's done a good job of it, and if Zendani is breaking with him that's another big knock on his base," said Krajeski.
Many in the US government are hoping Saleh survives "because we don't know what comes next," Krajeski said. "You can't come up with a good scenario that wouldn't be worse for Yemen."
He said that when he was ambassador to Yemen, the embassy did a report every year on who would replace Saleh if he were to suddenly disappear.
When they got to the conclusion, he said, "we came up empty."
He said there were people who the embassy thought would make good presidents, but "they just didn't have the support to get there.
"And the folks we thought might have it, we weren't really very pleased about that possibility. We'd just at the end say, we don't know."
"I think Ali Abdullah Saleh is in power for the immediate future, and when change happens, if it happens, we'll be the last to know," he said.