So where does that leave the FDA? the CDC?
I think the challenge based on the Origination Clause has a much better chance. Unlike Congress's power to legislate in the area of health care, there is not a lot of precedent wherein the Court has twisted the Constitution to mean what the Progressives want it to mean.
Obamacare is a revenue bill. Revenue bills must originate in the House. Obamacare originated in the Senate, after Dingy Harry did Select All, Delete, Paste, Save As on a House bill entitled the Service Members Home Ownership Tax Act of 2009. Therefore, because Congress didn't pass the law correctly, it must be tossed. The Origination Clause challenge is a do-over opportunity for Roberts. If he were to get it right, the law would simply be gone — regulations, mandate, taxes, and all.
The origination issue is a strong one. For everyone's benefit, here's a direct quote from Article I, Section 7 of the Constitution:
All Bills for raising Revenue shall originate in the House of Representatives; but the Senate may propose or concur with Amendments as on other Bills.
First note that any so-called "independent federal regulatory agency" is arguably unconstitutional under the Constituton's Sections 1-3 of Article I. That is because the Founding States made those statutes to clarify that all federal legislative powers are vested in the elected members of Congress, not unelected federal bureaucrats. In other words, Congress has a constitutional monopoly on federal legislative powers whether it wants it or not imo. And by unconstitutionally delegating federal regulatory / legislative powers to nonelected bureaucrats, Congress is wrongly protecting such powers from the wrath of the voters in defiance of the previously referenced statutes.
Regarding the FDA, I think that FDA should appropriately be an advisory agency to Congress under Congress's Commerce Clause powers. In other words, it's up to Congress to take responsibility for all laws and regulations relating to interstate food and drug commerce. And if voters don't like what Congress regulates then voters can kick federal lawmakers out of office and elect lawmakers who make laws that voters are willing to comply with.
Regarding the CDC, I think that the nation needs such a federal watchdog. But the states need to amend the Constitution to make CDC constitutional.
Regarding the EPA for example, not only does the EPA have no constitutional authority to tell anybody to do anything as per Sections 1-3 of Article I imo, but the states have never delegated to Congress via the Constitution the specific power to regulate the environment. So Congress not only wrongly established EPA, but delegated powers to it that Congress did not have.
Consider that the only reason that citizens and businesses reluctantly ask "How high?" when constitutionally toothless EPA shouts "Jump!" is because parents have not been making sure that their children are being taught about the federal government's constitutionally limited powers.
Regarding NASA for example, I've enjoyed following NASA for many years. But unless it's argued that NASA serves a military purpose which would justify it under Congress's Article I, Section 8-limited powers, NASA is another government agency that the states needed to amend the Constitution to give Congress the power to tax and spend for. And there is nothing stopping the Article V majority states from delegating such powers to Congress via the Constitution.
Finally, note that President Eisenhower needed to encourage Congress to petition the states for an amendment to the Constitution which would have granted Congress the constitutional authority that it needed to tax and spend to build the nation's highway system to improve the economy, a great idea. But consider that President James Madison had actually vetoed Congress's public works bill for building roads and canals, the 14th(?) Congress also wanting to boost the economy. In fact, although Madison agreed (paraphrased) in his veto letter to Congress that roads and canals would boost the economy, Madison also noted that his fellow delegates to the first Constitutional Convention had rejected a proposal to grant Congress, via the Constitution, the specific power to tax and spend for such purposes.
Veto of federal public works bill
Certainly the states would have ratified the required amendment to accomodate Eisenhower's vision for the nation. But note that low-information socialist FDR had previously wrongly ignored the Constitution's Article V when he established his New Deal spending programs. And Eisenhower was probably also a low-information voter who naively followed in FDR's footsteps like so many modern presidents have.