The same people who voted for opposition party also voted for the new Constitution. And that party was not a communist party. Some people say that Zhirinovsky was a FSB's project. In this case your ideas that US had anything to do with 12.1993 elections looks even more weird! Or stupid.
Yeltsin's support was very different in 1991 and in 1999. The problem was that Russia in 90s was still controlled by former communists/komsomol members, who were cynical, corrupt, brutal and terribly educated.
They didn't care about US and always tried to push pro-Russian ideas, check what Eltsin told to Clinton about Ukraine.. US had very limited involvement in internal politics, they just "hoped" that Russian will eventually become a normal country.
But when another stupid former communist Berezovsky decided to put his Puppet Putin into Kremlin - he failed miserably. KSB agent cannot do anything positive - his training is always about ruining and destroying, bringing lies and hate, stealing and bribing.