Russia had good reason to mobilize. Georgia was ratcheting up its attacks on South Ossetia and its violations of the previous cease fire, and the US and Israel were training and conducting military exercises with the Georgian military, as well as arming them rather massively (in proportion to the size of the country).

However, the Russians have not said that they moved into South Ossetia because the US was doing all of this in order to help the Republicans get their candidate elected. They have said they did it because of Georgia's attack on and invasion of South Ossetia.