They may be about to get their wish.
A report made public in Moscow this week supports widespread claims that the December 2011 parliamentary elections were falsified to hand the ruling United Russia party a slim majority of seats in the Duma.
The report, authored by a mathematician named Stepan Sulakshin, has garnered an unusual amount of attention because it was presented at a seminar overseen by Kremlin insider Vladimir Yakunin, the powerful chief of Russian Railways and a close confidant of President Vladimir Putin.
It also comes amid widespread chatter in the ruling elite that the Kremlin may seek early Duma elections as way to appease a restive public and to distance Putin from the increasingly unpopular United Russia party.
According to the report, the Communist Party came in first place in the elections with 30 percent of the vote, followed by United Russia with 22 percent. The center-left A Just Russia came in third with between 16-17 percent.
Official results had United Russia winning the elections with 49 percent, the Communists coming in second with 19 percent, and A Just Russia third with 13 percent.
Both the Kremlin and United Russia's leadership have dismissed the report -- at least publicly. But political analyst Mikhail Vinogradov told the daily "Kommersant" that there are some "zealous comrades" in Russia's ruling class who "believe it's necessary to quickly distance Putin from United Russia, so all the taint sticks to the party."
Likewise, "Kommersant," reported, citing unidentified Kremlin sources, that Putin's inner circle is considering the possibility of early Duma elections, which they hope will boost the president's ratings.
The appearance of the report -- and its association with Yakunin -- does strongly suggest that the issue of early Duma elections is being considered seriously.
"Yakunin is one of the pillars of the regime. He is particularly close to Putin and a member of the informal politburo," Valery Fedotov, a maverick member of United Russia from St. Petersburg who has a history of strained relations with the party leadership, wrote on the blogging platform Live Journal.
"Such a person would never go into opposition. It appears the authorities are launching a trial balloon and testing public opinion."
Fedotov added that if the Kremlin decided on new elections, it could lead to the absorption of United Russia into the All-Russian Popular Front -- an effective rebranding of the ruling party.
Another possibility, he said, was that the Kremlin would seek to heal the split in society by allowing a housebroken center-right party into the Duma.
Talk of new Duma elections, of course, comes at a time when Putin is clearly trying to reset the country's political arrangements, both formal and informal.
The on-again-off-again anticorruption campaign, the resignations from both houses of parliament, the "new deal" compelling officials to repatriate foreign assets, and now rumors of early elections suggest that less than a year after his inauguration, Putin feels the need to shake up and reorder a system that is no longer working for him.
"The young progressive section of society is demanding that Russia become a normal European country...Vladimir Vladimirovich is forced to maneuver constantly between these demands and the conservative masses who are demanding ever more blood," political analyst Igor Bunin told the daily "Moskovsky komsomolets."
"Putin has been behaving in an ad hoc manner, reacting to immediate challenges. He has been unable to construct a systematic pattern of behavior. He will have to offer something new."
In such a restive political climate, with a divided society and fractious elite, such a move is risky and could easily spin out of the Kremlin's control.
Elements of the elite with assets abroad, unhappy with the new rules Putin is imposing on them, could go off the reservation. The technocratic wing of the ruling class, which wants a thaw and is appalled with the hard line the president has adopted in his third term, could try to game elections to gain the upper hand.
And if the Kremlin wants to control the election results, that inevitably means shenanigans and falsification -- which could lead to more mass protests and greater unrest.
If Putin decides to go ahead with his reset, a new raucous political season could be about begin.
-- Brian Whitmore