In my mind no warrant should be necessary. Then again, I also believe thst failure to agree to a breathalyzer or fiekd sobriety test should be treated as an admission of guilt to a DUI/DWI.
The authorities will follow the mob, at the very least because this is a gray area. Anyway, an exception to the warrant requirement is if the evidence is being destroyed, including by metabolism, so no warrant would be required, if a drug test was justified.
It's not the nurse's right to use "policy" to disobey a police order. It's the cop's job to arrest people who refuse his instructions. It's a judge's job to decide of the evidence was illegally gained, in which case it can't be used to convict the person the evidence was taken from, and the office who illegally collected the evidence may be punished.
The mob defending the nurse are acting like savages in insisting that it's the right of the people to disobey police if they disagree with the police. That's also how people do get arrested and even killed by police.