It’s not obvious how many casualties the US itself would tolerate before going nuclear.
In circumstances where there were only a couple thousand American casualties, and those were incurred as collateral damage rather than as primary targets, it might make sense for the US to respond with conventional airstrikes and for Russia accept those and not escalate further.
This would depend a lot on the individual president though, like I could imagine Trump/Obama being much more risk averse than personalities like Bush 2 or JFK.