There's no way anyone could ever raise such an army. The US has 1,473,900 active personnel and 1,458,500 in reserve. The active personnel is just 0.8% of 170.5 million (which is approximately needed) and together the active and reserve personnel would only reach 1.7% of the personnel needed. Which would mean that you still need 167,641,600 men from allies. NATO with it's 28 countries could pitch in maybe 8,792,720 troops.
You could get with far less troops. I mean Russia is not very habited in some parts. 8.3/km2 is Russia's current population density. You would definitely get along with much much less troops than 170 million. If you said 10 soldiers per kilometre - now that would be more people than the total population of Russia, which is obviously not necessary. Like Hyperion said, much of it is forest. There's also tundra and steppe.