No they could not. That would lead to economic catastrophe worse than march/april 2020. Dems would get swept next election and the workers wouldn't even win because dems would be forced to pass this exact law within a week of the strike starting. The government can't let 100,000 unrelated people lose their jobs, and they really can't let grocery stores run out of stuff or coal plants run out of coal causing blackouts.
Fact is they hid behind the parliamentarian, insisted on bipartisan legislation as a priority and then proceeded to cede the power granted to make that excuse a reality today.
Personally, I reject it all and know damn well this could all play out differently and it doesn't because ordinary people are just not a priority.
As you say, they have their reasons for keeping it.
Your claim would be more useful if you pointed out the vote was 52-43; with no great effort six Republicans voted for it, five Democrats are AWOL and Manchin for some reason I can't imagine voted against it.
The Senate also voted 26-69 against 60 more days of negotiations.