According to Russian media, the only way a third term for Putin is still possible is if a constitutional amendment is passed by a large majority in the State Duma, the Federation Council, and among all of Russia's regional parliaments.
If President Putin were to change his mind and decide to run for another term, he would have no trouble getting the Consitution and the laws amended to do so. There is one dominant political party in power, United Russia, and it has more than enough votes in the national and regional parliaments to change the Russian constitution as it sees fit. Although Putin is not a member of United Russia, the party has always backed him unconditionally.
The government source told CBS News that Putin's advisors are split on whether the president should stay on. Some of Putin's closest advisors are lobbying him to change his mind and run for a third term, because they fear losing their positions and have no obvious candidate to replace Putin.
Kremlin research shows that if a referendum were held now, a majority of the Russian people would vote to keep Putin in office for a third term, according to the CBS News source.
If the Russian people voted for Putin to stay on and he did not, the president would risk putting himself and his successor in a very uncomfortable position. He would also risk damaging Russia's delicate international image, the Kremlin source said, if the people ask him to serve a third term as president and he refuses.