First, there is certainly no explicity power to tax any one that doesn't have health insurance in the Constitution. There are, of course, dozens of powers that aren't specifically enumerated in the constitution that are still used by the government. The Constitution is very specific in certain places and in other places it's very vague. So, it can be perfectly legitimate for Congress to draw power from any number of vague passages of the Constitution.
The power can come from one of two places. The first place is the Congress' power to regulate interstate commerce.
The Commerce Clause is an enumerated power listed in the United States
Constitution (Article 1, Section 8, Clause 3). The clause states that Congress has the power to regulate commerce with foreign nations, among the states, and with the Native American tribes.
Now, there's no question that health care is interstate commerce. Drugs are interstate commerce. Ironically enough, health insurance is NOT interstate commerce. That's because you can't buy health insurance across state lines. Yet, can the Congress force you to buy health insurance by the Commerce clause? To believe this you would have to have a very expansive view of government power. To believe this you would have to believe that your very participation in the health care system at all means that you are engaged in interstate commerce. In other words, you would have to believe that no specific act would be considered interstate commerce. Some people compare this to mandatory car insurance, but no one forces anyone to drive. The mandatory car insurance is for drivers only. Mandatory health insurance is for everyone. You would simply see health care as an interstate commerce endeavor and thus your very participation in it means that your behavior can be regulated. That views the power of the government as extremely expanded.
The second power from which to draw on is the Congress' power to tax.
The Congress shall have Power to lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States.
This power, as you can read, is very vague. It's left to interpretation. The difference between the Congress' prior power to tax and the proposal to mandate universal health insurance or face a penalty is that this would be the first time that Congress would tax you for action not taken. All prior taxes are on actions taken: income, sales, property, etc. As such, they are in a sense voluntary. No one is forced to buy anything and so you aren't forced into a sales tax. If a business loses money in a given year, they aren't taxed. In this case, the tax would be on action not taken. As such, each consumer would face fees either way. Either someone would pay for health insurance or they pay a tax. It would be the first time that the government would impose payment on an individual or impose a tax. That's never happened before. So, if you believe that such power is proper under the Constitution, then you view the Constitution as giving expansive tax power to the government.
So, while I believe the question of Constitutionality is open, there's no question that to believe that mandated health insurance is Constitution is to believe in a very expansive power to the government.