I was given an ultimatum like this once, to do X or resign, and I chose not to do X and refused to resign, and I worked there for an additional nine months until I found something better. I did have to endure several meetings where they kept saying I "needed" to resign or comply, but they never fired me. Said I would get a bad reference, but since that's extremely risky on the company's part, I still used them as a reference. HR dgaf. They just know they can't say anything negative about a previous employee. The whole thing is absurd posturing.