I think Putin can still give citizenship unilaterally, or the Russian Duma can.
But Barry and McCainer are claiming that Russia is helping Snowden to spy. So if they provide him with citizenship then that could be used against Snowden and Russia.
I copied and pasted 2 readers’ comments from the Moscow Times:
RetiredG
I wonder what Mr. Putin would do or say if the tables were turned and it was a Russian who had stolen and published some Russian intelligence and had landed in the USA?
disraeli
And if so, do you think the US would just hand over to Russia such a person?
If I were Putin, I'd make Snowden a non-extradictable citizen of Russia. And, as for employment, I'd hook him up with my fellow KGB-alum Eugene Kaspersky, of consumer anti-virus fame (LOL). The idea: create a Kremlin-funded subsidiary aimed at vacuuming the US dry.
Tour of Kaspersky Labs [video]
Around the world, an estimated 12 million individuals lack nationality or citizenship in any nation. (link)
There are international agreements about dealing with stateless persons, refugees and people who are politically or religiously persecuted.
Obviously, no action of their former government - such as revoking the passport - can hurt the status of the refugee. It can only prove, very clearly, that their old government is really after them, and that the refugee should be accepted.
There is no extradition treaty between the USA and Russia. Why? No time to sign a standard paper? Who dragged their feet? Was it the US Government because it wanted to play the card of Russian emigrants? Hardly any US citizen escapes to Russia - until now, that is - so Russia could not have the same motivation toward the USA. Plenty of Russian criminals left Russia to live comfortably in UK or here, and Russia would like to have them back. Some Chechen warmongers still live in London; don't know how safe they feel, though :-)
Now this lack of extradition treaty hurts Obama. He cannot claw Snowden back. I think Putin will give Snowden another week to try to leave, and after that predictably fails (where'd he go without a passport, short of a direct flight to Equador?) Putin will issue him a temporary visa on humanitarian grounds, which for some obscure reason will never expire. He will get a nice job, of course, and - being young enough to relocate with ease - will just continue living and working. I'm sure he is smart enough to be productive. He is good with foreign languages, as you'd expect. By the way, he is not married - yet.
And besides, it's obvious that if he ever makes it to Equador, how safe will he be in the US backyard? His residence there would be measurable in days; weeks on the outside. But it would be far more difficult for the CIA to remove a person from Russia; he actually has a chance there.
If Ecuador approves his asylum they can issue him an Ecuadorian passport.