alison, the US Joint Chiefs drafted a set of war plan scenarios in 1949 in expectation for war in 1957. One premise was a US first strike with B29s in cells with, IIRC, 2 weapons carriers and 7 escorts and decoys.
Having successfully attacked Russia they then examined the potential consequences. These included immediate capitulation and the need to occupy the USSR with own forces that were not fully mobilised. US forces would therefore have to consider commanding surviving defeated Soviet forces to garrison and recover post-strike.
Awesome stuff but no doubts that they would have attacked or countered Soviet attacks. If you want to read the plans look for Plan Dropshot.
https://en.wikipedia.org/wiki/Operation_Dropshot