Agreed...
This would never happen. There's no national union for nurses. The only place that I'm aware of that has a nurse union is California. They strike all the time, but there are plenty of nurses willing to replace them while they are striking, so no real I'll effects from this. Now, there could be other states with unions, but I'm not familiar.
To strike during a national emergency would warrant losing your job, title and retirement, in my opinion. On a case by case basis, it's okay for medical personnel to refuse things based on personal safety and the potential for harm (asking you to take care of a suspicious patient when you don't have the proper PPE), but generally, no.
The air traffic controllers Union screwed the pooch years ago when they went on strike. They had a gravy train job, made good money, and could retire with full benefits after 20 years. ( Think about it. You could be an air traffic controller without a a degree. So, at 20 years old you could start your career as an air traffic controller and retire at 40 with full benefits. They were making upwards of $100,000 a year 30 years ago) But, that wasn't enough. Reagan, appropriately, gave them an option and if they didn't comply they were told to hit the bricks and lose everything. Many did and I'm sure regret it to this day if they are still alive.
*I know the ATC strike was more than 30 years ago...I'm just using that time frame for reference.