Snowden, after blowing the lid off US phone and Internet surveillance programs, has evaded the combined might of the White House, the US intelligence community and the long arm of US justice.
After sifting their political options, Beijing and Moscow apparently decided that bailing Washington out was not in their best interests - and refused to expel him to America after he landed on their soil.
The optics are uncomfortable for a White House lashed by critics for presiding over ebbing US power abroad.
The drama exacerbates the deep embarrassment Washington is feeling after seeing its National Security Agency (NSA) eavesdropping programs exposed to the world by Snowden's leaks.
Obama's personal discomfort is compounded since he sat down with both Chinese President Xi Jinping and Russia's Vladimir Putin recently, hoping to smooth perilous relations.
Putin on Tuesday said Russia had no grounds to expel Snowden - from his latest bolt-hole in Moscow airport - as it did not have an extradition treaty with the United States.
He also said authorities had no idea in advance that Snowden would flee from Hong Kong from Moscow - a comment met with skepticism in Washington where it is assumed China and Russia have drained Snowden of useful intelligence.
"The bottom line is the United States and the Obama administration are left holding the bag, looking straight at a major breach of intelligence with few tools if any to resolve the situation," said Andrew Kuchins, a Russia analyst with the Center for Strategic and International Studies.
"The whole thing is very embarrassing."
It seems unlikely the White House seriously expected either rival to return Snowden, but politically, it has little option but to put up a fight.
On Tuesday, it chose to extend the standoff with Moscow, telling Putin there was a clear legal basis for Moscow to expel him.
Domestic pressure on Obama meanwhile is mounting.
Republican Senator John McCain said Russian behavior was reminiscent of the Cold War and blamed Obama's "leading from behind" statesmanship.
"(Putin) is an old KGB colonel apparatchik that dreams of the days of the Russian Empire and he continues to stick his thumb in our eye," McCain told CNN.
Former Bush administration official Peter Wehner declared on the Commentary website that Putin had exposed Obama as an "irresolute amateur."
The Obama administration faces a delicate decision on its response.
The Justice Department, FBI, White House and State Department are doing everything legally and politically possible to chase Snowden.
But their efforts are serving only to show the limits of US reach.
Russia and China meanwhile are vital to many of Obama's second term priorities: containing North Korea, ending the Syria crisis, Iran's nuclear challenge and his call for new nuclear weapons cuts, to name a few.
So there may be a case for trying to contain long term damage.
Still, Putin's actions, and demeanor at a summit with Obama last week in Northern Ireland, suggest he has concluded Washington needs him, more than he needs Obama.
Moscow may also be exacting revenge for the US refusal to extradite arms dealer Viktor Bout, and over the Magnitsky Act, which punishes officials deemed guilty in the murder of a Moscow lawyer.
Given unpromising prospects of getting Snowden back, the White House has chosen not to deploy Obama's personal prestige - he spoke generally about the rule of law when asked about the episode on Monday.
The fulminating has been left to White House spokesman Jay Carney, who warned Monday the White House did not "buy" the claim that a Hong Kong immigration official, and not the government in Beijing, let Snowden flee.
"That decision unquestionably has a negative impact on the US-China relationship," Carney said.
For now, the White House is distinguishing between the actions of China - and Russia, possibly because Snowden is still in Moscow.
National Security Council spokeswoman Caitlin Hayden told AFP the White House did not want Snowden to "negatively impact" relations with Russia.
Washington also courted Russia's law enforcement community, and cited good cooperation since the Boston bombing.
Republican Senator Tom Coburn said the White House would likely exact revenge on China meanwhile on the quiet.
"The next time they really need something that only we can deliver, it probably isn't going to happen," Coburn told MSNBC. "But it's not going to be published. We're not going to embarrass them."