But even if all 20 export projects were approved today, it would take years—and several very cold and dark European winters—before U.S. exports would have any meaningful impact on European supplies.
Still, with its economy weakening, Russia also can ill-afford any crimp in the supply of its biggest source of already-scarce capital.
Russia's heavy reliance on the cash from oil and gas exports is something of an Achilles heel for the Kremlin because the Russian economy depends heavily that hard currency to buy manufactured products from Europe—and around the world.
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Some 70 percent of the country's exports are related to energy and mining, while Russia imports roughly 80 percent of manufactured goods, according to the latest figures from the World Trade Organization. About a third of those imports—everything from vehicles to computer equipment—come from Europe.
And with a relatively small manufacturing base, Russia's economy is also highly vulnerable to canceled orders from U.S. and European customers. Some Russian companies are already feeling the chill of a drop in demand, according to Philip Uglow, chief economist at MNI, based on his firm's survey this month of 200 large Russian companies.
"What we've heard from Russian companies this month is that they're seeing a big fall in export orders," he said. "Certainly their seeing some pain for the tension in Ukraine. They probably fear most trade or financial sanctions."
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Extending the U.S. and European asset freeze beyond the current handful or Putin's political cronies would inflict additional pressure on Putin. That's because the cash accumulated by Russian oligarchs is also one of Russia's biggest exports.
"Sanctions that really targeted the banking system the same way that U.S.. sanctions went after Iran, that could have a significant effect," Uglow said. "But that really requires a huge shift about pushing Russia away from the world economy as opposed to in it."
It also means convincing global financial companies, with strong political connections in Washington, London and Berlin, that containing Russian aggression in a capital-poor country like Ukraine is worth a substantial hit to the industry's bottom line.
"Fairly narrow targeted financial sanctions have been put forward, but a number of international financial interests are ready to get back to business as usual, which is often as is the case," Stephen Yates, CEO at DC International Advisory, told CNBC. "So Putin sees himself as having weather the wave, and so now onward and upward with whatever his agenda may be."
Organizing global economic sanctions is never easy, but the large outflows of Russian wealth parked around the further complicates the process. Without strong European cooperation, the U.S. will have a tough time tightening the economic noose, according Rep. Kevin Brady, R-Texas, chairman of the Joint Economic Committee.
"Traditionally Europe likes us to play the bad guys," he told CNBC. "That won't work in this case. The banking relationships in London, the business relationships across Europe, and the oligarch investments they've made are numerous."
The outflow of Russian cash has only picked up since the turmoil in Ukraine began. Russian officials have said the capital flight could hit $70 billion for the first three months of the year—more than the $63 billion that fled the country in all of last year.
"Unless there is more clarity, this outflow will continue, major business decisions are likely to be halted and potential commercial opportunities can be lost for Russia, all ultimately adding to Moscow's overall economic losses," IHS Global Insight Senior Economist Lilit Gevorgyan said in a note to clients.
Russia's economy call ill-afford to see more capital head for the exits. Though energy exports rebounded following a deep slide during the global recession, overall gross domestic product began slowing last year and is weakening further. Last year, GDP growth fell to 1.3 percent from 3.4 percent in 2012.
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It was the fourth year of slowdown for the $2 trillion economy, as growth in consumer spending was offset by a pickup in capital flight and a drop in global oil and natural gas demand.
MNI's Uglow figures Russia's GDP growth will fall below 1 percent for the rest of the year. And he said that Russian companies, which have been benefiting from a drop in the ruble that make their products more attractive in overseas markets, now fear that the currency is weakening too quickly.
"What it's demonstrating is more economic instability in Russia," he said. "That could be a worry if it falls too far and too fast."
