The terms "Russians" and "Soviets" were used interchangeably within the American government (and State Department), at least during LBJ's administration, when talking about Soviet foreign policy. See, for example, this policy paper written by Walt Rostow in 1968 written for the State Department/LBJ's administration in which he mostly refers to the "Soviets," but also notes that the "Russians must be hesitating," all while analyzing Soviet policy towards Czechoslovakia. Also look at this conversation between Secretary of State Dean Rusk and future president Richard Nixon, in which Rusk also refers to them as both "Soviets" and "Russians" (again, without clear distinction in meaning; note is is possible here in this 2nd source that the note-taker Tom Johnson picked the words, but this would not undermine the point).

Typically, however, when speaking or writing formally, the term "Soviet" was preferred (calling them "Russians" was a somewhat colloquial way to refer to them, somewhere between "Ruskies" and "Soviets," though far more proper than "Ruskies"). See, for example, this letter from Rusk (the same Rusk) to the Czechoslovak embassy, in which he uses the term "Soviet" 9 times, the term "Russian" no times. And see this conversation between Rusk and the Soviet Ambassador Dobrynin where the term "Soviet" is also used exclusively, despite the fact that Dobrynin himself was ethnically Russian (i.e., it just wasn't proper to refer to the "Russians" in front of a Soviet dignitary).

These documents reflect typical usage during LBJ's years. All of these documents are provided by the State Department's Foreign Relations of the United States series, the official documentary historical record of major U.S. foreign policy.

I notice you use "Russians" and "Russia". Note that the USSR included Ukraine, Lithuania, Armenia and dozens of other national polities - I hope you don't ever call them Russians!

Russia (the "Russian Soviet Federative Socialist Republic") was technically from 1922 to 1991 just one - though by far the largest - republic in a federal state. So it's worthwhile to disentangle the terms, just practically apart from any ideological inclinations.

But obviously you mean what its government termed the USSR. Those more sympathetic to the eastern side were more likely to use "Soviet" (the strictly correct term as the USSR included many non-Russians, some in positions of power - even Stalin was a Georgian, not a Russian); those less well-disposed or seeking to portray the USSR as merely a revived Russian empire were likely to prefer the R-word. But it's a bit more complicated, because even at the height of the WW2 US-Soviet-British alliance "Russian" was far more common in the West even among those embracing the USSR in a common cause. So part of it's probably down to traditional usage, presumably from the pre-1917 days of the Russian Empire, which covers a similar area and also incorporated many non-Russian peoples - thus the "Our Russian ally" of 1914 could readily be re-used in 1941. It's difficult to disentangle when the term is being used pejoratively or merely as anachronistic shorthand.

Among those strictly non-aligned between west and east, I think "Soviet/USSR" was more common, just because that's how the country's government styled itself.