Right now, if high net worth individuals pay insurance at all (it's usually an employer provided benefit), it's pre-tax and even the best cadillac plans for the entire family are ~2k/mo. A 10 percent increase in income tax would rankle anybody making over ~150k/yr, and that's assuming the best whole family plans. Someone like myself who pays under 400/mo for really good insurance would get dinged on a 10 percent tax increase at only $50k/yr.
Single payer would have to come in at about a 5-7 percent tax increase for it to be even remotely palatable to me, and that's as someone who's all for it and think it's morally bankrupt that we don't have it.
The average person in the US is already paying ~200% as much as a citizen of your typical single-payer country for coverage. Not only are we paying twice as much for coverage, we don't even have universal coverage after paying twice as much.
The health care tax could be regressive, say 5-10% of your income below first $100-150k, and then 0% of the remainder. This way, even the richest would not be affected that much by that additional tax.
Actually, even without additional tax, if US government dropped Medicare, Medicaid and other state sponsored insurance systems in favor of universal coverage, it would have enough money to have world-class healthcare system without any additional taxes -- the US government _already_ spends as much on health care per capita as Germany, or France, and 30% more than UK.
Single payer would have to come in at about a 5-7 percent tax increase for it to be even remotely palatable to me, and that's as someone who's all for it and think it's morally bankrupt that we don't have it.