Short answer: probably.
Long answer: It depends what you mean by calling something "constitutional". If we define (Def. A.) constitutional as meaning in line with the Supreme Court's commerce clause jurisprudence over the last 200 years, then I would say, probably. If we define it as conforming to some originalist conception of the limits of the federal government held by the founding generation (Def. B.), I would say, we can have no idea. If we define it as what a majority of justices on the Supreme Court will do when it gets there (Def. C.), I think we can still say they'll probably count it as constitutional.
A and C involve almost the same thinking process, because typically if something conforms with 200 years of jurisprudence, the Supreme Court will rubber stamp it. But that's not always true, and the justices are not isolated apolitical creatures who remain uninfluenced by the national debate. Just like all 9 Justice could vote in favor of the measure, I can definitely see all 5 conservatives voting against it. I don't think that will happen, however, as I will discuss.
So, the problem with the individual mandate (IM) is that it apparently forces individuals to purchase health insurance from entities that meet certain criteria. Opponents of the IM who argue that it is unconstitutional (Opponents) argue that the constitution does not authorize the federal government to force individuals to purchase anything.
So, one response is just to say that the federal government is not forcing you to do anything. The government wants you to buy health insurance. If you do, good on you. If not, the government wants you to pay a fine or tax, the moneys of which will go into the pool of money which funds the government's expenditures on health, presumably towards treating people without health insurance. The fine or tax is not that much, and can't exceed, I believe, 2.5% of your income. Also, there's a provision that forbids the IRS from starting criminal proceedings against anyone who doesn't pay the fine/tax, so you can't go to jail if you don't pay it.
I don't particularly like this argument, because I'm not sure how a court will look at this. It could be that in this instance, there's no coercion, but then the Court would have to examine future instances, looking at the substance of the law and its enforcement mechanisms, to see if counts as coercive or not. Is 3% coercive? 10%? I'm not sure where one draws the line, or on what grounds one would draw it.
A much better argument is that the constitution allows the federal government to tax really whatever it wants, provided it's for the general welfare, which Obamacare certainly is. Opponents have argued that this is not the way that either Congress or the Administration have been framing it; they've been calling it a mandate (connoting the fact that people must do something) and not a tax (a collection of revenue from people who choose to engage in certain activities, in this case, not buying health insurance). FWIW, this makes little sense to me. What does a Court care about how the Democrats framed something for political debate or Sunday morning talk-shows? The court will look at it, see it's a tax, and call it as such. Try a thought experiment. If the government decided to kill people randomly, but labeled it a carbon tax in all its attempts at spinning the law to the press, would we think it makes sense for the government to consider it a carbon tax, and not the random murder of citizens?
But I think a more fundamental reason why the constitution authorizes it, is because the government's power to regulate interstate commerce is pretty strong. One argument opponents make is that as strong as the commerce clause is, it's never been used to force people to perform actions when they're not doing anything. In other words, government can't regulate interstate inactions, just interstate actions. People always ask, "Can the government force me to buy a GM car, or force me to eat my vegetables?"
Okay, let's break this down. Let's assume that the government has never attempted to regulate inaction. So what? Why should that make a difference? It's never been questioned before that the government can't regulate inaction - what's the constitutional reason why government can't regulate inaction now?
So then we get to the idea that if the government could regulate inaction (i.e. forcing you to do things), then we would be empowering if not a tyrannical government, then at least a government with a loaded gun, which could be used to launch a tyranny at some point. Imaigne a dystopia where the government forced you to eat vegetables or buy crappy GM cars! Surely, the constitution does not authorize dystopias? However, honestly, I'm not sure why not. If the government can make a compelling case that you buying a GM car is necessary or helpful, even, to its national commercial regulatory scheme, it seems clear to me it can force you to buy a GM car. This may be exceedingly dumb policy and prove to be very unpopular, but the constitution authorizes scores of dumb and unpopular policies.
The reason why the government (probably) won't force you to eat your vegetables is not because the constitution does not authorize it, but because Congressmen don't want to get fired. If 60% of the House of Representatives and the Senate think an IM is a good idea, then as far as the constitution is concerned, it's probably a good idea. That is, the constitution does not care if something is a good idea or not. If those democratically elected representatives want to roll the die on their careers, I'm largely comfortable letting them make that choice.
We have to get over the idea that the constitution protects us from tyranny and bad policy. In reality, it's us. When push comes to shove, what stops a military junta from taking power is not Congress's theoretical control over its funding, but the fact that the common man, and the common soldier and officer, would see such a coup as illegitimate.