The larger companies, particularly the public companies, already provide health care to their employees. They won't be paying this tax.
It's the smaller companies that will pay the tax. They're more likely to provide health care to their employees instead of paying the tax, which is the point of the new tax, after all--to goad them to do that. A lot of these smaller companies aren't going anywhere because they do things like construction and services that need to be done here. They'll end up passing some of the costs on to the consumer.
I hate to tell you this but probably most areas of the US suck for jobs if you don't already have money or don't know a profession.
As for FL having a higher tax rate than NH: We have no income tax, I pay a 7% sales tax in my county and I pay $1100 a year property tax on a house worth $250k.
Like NH, we also have some toll roads.
I know my aunt and uncle have to pay an arm and a leg for property taxes to live in NH.
The smaller companies you speak of that will pass "some" of the tax on to consumers will pass all of it or hire more illegals. Illegals that you will still pay for health costs.