I wouldn’t be pissed if the President didn’t order a retaliatory strike - I would be pissed if he did. Wiping out Russia isn’t going to bring anyone back to life, or repair any damage - just make everything worse, for no good reason except revenge. Like Habeed says, the deterrent didn’t work,. OK, next time better try something else.
Of course the scenario probably wouldn’t work out like that. Their first strike would be an attempt to take out our missiles, as well as our command and control. That’s why we have sub-launched missiles, because the Russians probably could not target them effectively enough to ensure that the US could not retaliate and take out as many of their missiles as they did ours. In that case I probably would retaliate, to try to prevent them from a second-strike.
In practical terms, it wouldn’t make that much difference. Taking out missile sites means killing lots of people even if that is not the primary objective, and even more so with targeting command-and-control.
As far as the question if the generals would counter-attack if the President didn’t order it, I thought the purpose of the football everyone talks about is to prevent anyone but the President, or the Vice-president in event of the President being dead or incapacitated, from launching the Bomb. I hope and expect that the launch codes are necessary not only to authorize an attack, but to enable it.