It is the first time in history that the US have lost their opening two qualifying games.
A brutal 4-0 mauling by Costa Rica on Tuesday in San Jose, just four days after a shattering 2-1 loss to Mexico in Columbus on Friday, has left the US rooted to the bottom of CONCACAF's six-team final qualifying group.
It is the first time in history that the US have lost their opening two qualifying games, and the first time since 2001 that they have lost back-to-back fixtures during the qualifiers.
"This is the defeat that hurts the most in my five years here, there's no doubt about it," Klinsmann said after Tuesday's defeat, the heaviest US qualifying shutout since a 6-0 loss to Mexico in 1957.
"It is a bitter pill to swallow."
For now, Klinsmann's employers at the United States Soccer are keeping their own counsel on the coach's future.
"We won't make any decisions right after games," US Soccer chief Sunil Gulati said following the Costa Rica drubbing. "We'll think about what happened today and talk with Jurgen and look at the situation."
But for Klinsmann's sizeable legion of critics amongst the ranks of pundits and US-based press, the defeat was final confirmation that the German's time is up.
Tuesday's loss was the latest in a series of setbacks that have dogged Klinsmann's reign in the two years since his team returned from the 2014 World Cup as heroes after reaching the second round, where they qualified from a "Group of Death" which included Germany, Portugal and Ghana.
A failure to win the 2015 Gold Cup on home soil, when his team was eliminated in the semi-finals, was followed by defeat to Mexico in a play-off to determine CONCACAF's representatives at the 2017 Confederations Cup in Russia.
Although Klinsmann's men enjoyed a respectable Copa America Centenario campaign in June, the gloss was taken off their run to the semi-finals by the manner of their defeat in the last four, when they were soundly beaten 4-0 by a Lionel Messi-inspired Argentina.
Klinsmann looked to have quelled the critics during preliminary rounds of the World Cup qualifiers, where the emergence of rising stars such as Christian Pulisic and Bobby Wood provided cause for optimism.
But doubts about Klinsmann's management style and tactical savvy were reawakened last week in Columbus, when he opted for an unfamiliar 3-5-2 system against Mexico to the obvious discomfort of his players.
The system was abandoned midway through the first half but by then Mexico were already 1-0 up and would go on to win the game 2-1.
"It's time for Jurgen Klinsmann to go," was the blunt verdict of Sports Illustrated's football correspondent Grant Wahl, arguing that the "calculus has changed" in the wake of the losses to Mexico and Costa Rica.
Fox Sports soccer writer Ryan Rosenblatt described Tuesday's defeat as "arguably the United States' worst loss of the modern era."
"By Friday, he may not have a job and, frankly, he shouldn't. There is no reasonable case to be made anymore that Klinsmann should continue as the US manager," Rosenblatt wrote.
Former USA striker Brian McBride wondered whether Tuesday's defeat indicated that Klinsmann's players no longer had confidence in his reign.
"Has Jurgen lost the locker room? Are players playing for him?," McBride said on ESPN.
"I think at the end of last night I was questioning many things. There needs to be a serious conversation (about Klinsmann's future)."
Klinsmann may ultimately be saved by the dearth of obvious replacements. Former coach Bruce Arena is being championed in some quarters, but would be regarded as a retrograde appointment by others, while 2010 World Cup coach Bob Bradley has only just started in the Premier League with Swansea.