Russia's financial system has been badly affected by the global economic crisis, with record losses on its financial markets, rising interest rates and a liquidity shortage.
Communist Party MP Vadim Solovyov said the Russian economy had started to take "heavy blows."
"We think the Finance Ministry and the minister himself are directly to blame," he said, accusing the ministry of using the proceeds of Russian oil and gas exports to buy foreign assets instead of supporting domestic businesses.
"Small enterprises and entrepreneurs have also taken loans, so it [crisis] can lead to a series of failures among small and medium businesses, millions of people will find themselves jobless, and that will lead to enormous social tensions," he said.
"We are half a step away from a default," Solovyov added. "Our entire economy could collapse overnight."
Sergei Mitrokhin, leader of another opposition party, Yabloko, condemned the "inaction, placidity and giddy optimism of the Russian government," which he said together with the global financial crisis had led to economic problems in the country.
The opposition worries have been echoed by Russia's labor unions warning of increasing social tensions.
Mikhail Shmakov, head of the Federation of Independent Trade Unions of Russia, said that "street protests will increase" following job losses, which will be caused by investments cuts.
"Today we demand that the government, first of all the Finance Ministry, take urgent measures," Shmakov said.
At a Kremlin meeting Tuesday, President Dmitry Medvedev pledged to give banks extra 950 billion rubles ($36 billion) in credit for terms of at least five years to support the financial sector.
The move followed an almost 20% plunge on the Russian stock market Monday.
