Yes, it would make perfect sense. In theory, we have 1/6th of the population without health insurance. If they all went out and bought insurance, it would reduce our premiums. Also, according to the Economist magazine, the US subsidizes emploer paid insurance premiums pre-tax at about $250 billion annually.
Since you can't force people to buy, you can force taxes.
Therefore, add to the payroll tax the % needed and cap it off for anyone who makes more than 150,000/yr (In theory, the rich do not need to be taxed for health costs that they will never use. Same logic is used for Social Security benefits).
Those who pay premiums now, will most likely see the tax repalce their premiums paid.
Those who were not paying, will now have to pay.