But some analysts think it's a doomed strategy. "It is the wrong time for the Greek government to believe, with all the problems that it has, that it could be a catalyst in the formation of a new EU-Russia relationship," said Nikos Meletis, diplomatic correspondent for Ethnos, an Athenian newspaper. "The government has miscalculated and overestimated its role at a moment when everyone sees Greece, because it has run out of money, as a kind of Trojan horse for Putin."
The reality is that the Russians can't help the Greeks in the short term, anyway, even if they wanted too. Russia has its own economic troubles. The desire to help financially may not be there, either—when Cyprus approached Russia for help in 2013 during its own banking crisis, for example, Russia did not come forward with any assistance.
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The only bright spot, according to analyst Tzogopoulos: Tsipras' Kremlin visit provided encouragement to Russian companies to participate in privatization bids for Greek assets down the road.
Even Foreign Minister Kotzias in his comments to CNBC acknowledged that the Russians weren't going to solve Greece's severe short-term financial troubles. The talks with Gazprom, he argued, and the possibility of the company sharing its profits with Greece down the road are only part of a solution to Greece's long-term development. "This is not part of a solution to the debt crisis," he said. "Russia cannot give us a solution to our problem."
That solution, argued Kotzias, lies in the hands of Europe—and he is optimistic that a solution will be found through compromise.
In essence, then, no matter how much Tsipras and his party leaders would like to play the international geopolitical poker game to their own domestic advantage, indeed even their own political survival, Europe has the stronger hand.
Even a deal with Russia over a gas pipeline, if indeed it ever gets finalized, ultimately will need the approval of the European Union. Said analyst Tzogopoulos: "The EU has the last word." In the latest chapter of the Greek financial saga, it most certainly appears that way.
—By Dody Tsiantar, special to CNBC.com