There is much to digest here, but the following points seem salient. The following quotes are organized by the Justice or Justices who authored the opinoins:
Justice Roberts emphasized that the deployment of an economic mandate was unprededented:
Given its expansive scope, it is no surprise that Congress has employed the commerce power in a wide variety of ways to address the pressing needs of the time. But Congress has never attempted to rely on that power to compel individuals not engaged in commerce to purchase an unwanted product.3 Legislative novelty is not necessarily fatal; there is a first time for everything. But sometimes “the most telling indication of [a] severe constitutional problem . . . is the lack of historical precedent” for Congress’s action.
And Roberts relies on the activity/inactivity distinction:
The individual mandate, however, does not regulate existing commercial activity. It instead compels individuals to become active in commerce by purchasing a product, on the ground that their failure to do so affects interstate commerce. Construing the Commerce Clause to permit Congress to regulate individuals precisely because they are doing nothing would open a new and potentially vast domain to congressional authority. Every day individuals do not do an infinite number of things. In some cases they decide not to do something; in others they simply fail to do it. Allowing Congress to justify federal regulation by pointing to the effect of inaction on commerce would bring countless decisions an individual could potentially make within the scope of federal regulation, and—under the Government’s theory—empower Congress to make those decisions for him.
To an economist, perhaps, there is no difference between activity and inactivity; both have measurable economic effects on commerce. But the distinction between doing something and doing nothing would not have been lost on the Framers, who were “practical statesmen,” not metaphysical philosophers.
In discussing the Necessary and Proper Clause, Justice Roberts relied on the argument that the mandate was not "proper":
[W]e have also carried out our responsibility to declare unconstitutional those laws that undermine the structure of government established by the Constitution. Such laws, which are not “consist[ent] with the letter and spirit of the constitution,” McCulloch, supra, at 421, are not “proper [means] for carrying into Execution” Congress’s enumerated powers. Rather, they are, “in the words of The Federalist, ‘merely acts of usurpation’ which ‘deserve to be treated as such.’”
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Even if the individual mandate is “necessary” to the Act’s insurance reforms, such an expansion of federal power is not a “proper” means for making those reforms effective.
Justices Scalia, Kennedy, Thomas, and Alito
The joint opinion of the four dissenters includes the following remark about the Court's recent congressional power cases:
The Lesson of [New York v. United States, Printz v. United States, United States v. Lopez, and United States v. Morrizon] is that the Commerce Clause, even when sup- plemented by the Necessary and Proper Clause, is not carte blanche for doing whatever will help achieve the ends Congress seeks by the regulation of commerce. And the last two of these cases show that the scope of the Necessary and Proper Clause is exceeded not only when the congressional action directly violates the sovereignty of the States but also when it violates the background principle of enumerated (and hence limited) federal power
And with respect to Gonzales v. Raich:
Raich is no precedent for what Congress has done here. That case’s prohibition of growing (cf. Wickard, 317 U. S. 111), and of possession (cf. innumerable federal statutes) did not represent the expansion of the federal power to direct into a broad new field. The mandating of economic activity does, and since it is a field so limitless that it converts the Commerce Clause into a general authority to direct the economy, that mandating is not “consist[ent] with the letter and spirit of the constitution.”
And on the question whether the Government's theory of the case involves a well-defined limit on federal power:
The Government was invited, at oral argument, to suggest what federal controls over private conduct (other than those explicitly prohibited by the Bill of Rights or other constitutional controls) could not be justified as necessary and proper for the carrying out of a general regulatory scheme. See Tr. of Oral Arg. 27–30, 43–45 (Mar. 27, 2012). It was unable to name any. As we said at the outset, whereas the precise scope of the Commerce Clause and the Necessary and Proper Clause is uncertain, the proposition that the Federal Government cannot do everything is a fundamental precept.
And on the activity/inactivity distinction:
Wickard v. Filburn has been regarded as the most expansive assertion of the commerce power in our history. A close second is Perez v. United States, 402 U. S. 146 (1971), which upheld a statute criminalizing the eminently local activity of loan-sharking. Both of those cases, however, involved commercial activity. To go beyond that, and to say that the failure to grow wheat or the refusal to make loans affects commerce, so that growing and lending can be federally compelled, is to extend federal power to virtually everything. All of us consume food, and when we do so the Federal Government can prescribe what its quality must be and even how much we must pay. But the mere fact that we all consume food and are thus, sooner or later, participants in the “market” for food, does not empower the Government to say when and what we will buy. That is essentially what this Act seeks to do with respect to the purchase of health care. It exceeds federal power.
And also on activity/inactivity:
It is true enough that Congress needs only a “‘rational basis’ for concluding that the regulated activity substantially affects interstate commerce,” ante, at 15 (emphasis added). But it must be activity affecting commerce that is regulated, and not merely the failure to engage in commerce. And one is not now purchasing the health care covered by the insurance mandate simply because one is likely to be purchasing it in the future. Our test’s premise of regulated activity is not invented out of whole cloth, but rests upon the Constitution’s requirement that it be commerce which is regulated. If all inactivity affecting commerce is commerce, commerce is everything.
Justices Thomas's Opinion
Here is the key passage:
I adhere to my view that “the very notion of a ‘substantial effects’ test under the Commerce Clause is inconsistent with the original understanding of Congress’ powers and with this Court’s early Commerce Clause cases.”
Justice Ginsburg's Opinion:
Justice Ginsburg's opinion strongly emphasizes the rational basis test in conjunction with the effects doctrine:
Beyond dispute, Congress had a rational basis for concluding that the uninsured, as a class, substantially affect interstate commerce. Those without insurance consume billions of dollars of health-care products and services each year. See supra, at 5. Those goods are produced, sold, and delivered largely by national and regional companies who routinely transact business across state lines. The uninsured also cross state lines to receive care. Some have medical emer gencies while away from home. Others, when sick, go to a neighboring State that provides better care for those who have not prepaid for care. See supra, at 7–8.
And on the activity/inactivity distinction:
Nor does our case law toe the activity versus inactiv ity line. In Wickard, for example, we upheld the penalty imposed on a farmer who grew too much wheat, even though the regulation had the effect of compelling farmers to purchase wheat in the open market. Id., at 127–129. “[F]orcing some farmers into the market to buy what they could provide for themselves” was, the Court held, a valid means of regulating commerce. Id., at 128–129. In an- other context, this Court similarly upheld Congress’ author ity under the commerce power to compel an “inactive” land holder to submit to an unwanted sale.
And on the argument that the mandate is unprecedented:
For decades, the Court has declined to override legislation because of its novelty, and for good reason. As our national economy grows and changes, we have recognized, Congress must adapt to the changing “economic and financial realities.” See supra, at 14–15. Hindering Congress’ ability to do so is shortsighted; if history is any guide, today’s constriction of the Commerce Clause will not endure. See supra, at 25–26.