If you're completely swamping private insurance, though, then payroll tax hikes should be a net zero, though i guess that depends on how closely the salary:benefits ratio tracks with payroll tax rates.
Say if payroll tax was 15% and your health benefits were 33% of your gross salary, then an 18% hike in payroll tax would mean that nothing changed, the money just goes to the government instead of the insurance company, and if your insurance was partially employee funded (e.g. employee had to pay 20% of monthly premium), it's a net win for the employee who gets that money in their pocket.
But that depends, like i said.