In NFIB v. Sebelius, the votes were unusual. Five justices held that the ACA's mandate could not be supported by Congress's commerce powers. Five justices also held that under the best reading of the statute, the penalty enforcing the ACA's mandate cannot be construed as a valid exercise of the taxing power. Chief Justice Roberts, however, used these findings of unconstitutionality as a necessary predicate to applying the saving construction.
This part of the opinion is not well-understood. Some critics charged that Roberts's analysis of the commerce clause was unnecessary since he ultimately upheld the law as a valid exercise of the taxing power. The speculation was that Roberts wanted to gift conservative some jurisprudential victory on the Commerce Clause while upholding Obamacare. The Chief Justice could only get to the saving construction after fully considering whether the law was otherwise unconstitutional. Under the saving construction, the Chief Justice was able to construe the penalty as a tax. To be sure, Roberts acknowledged the saving construction wasn't the best reading of the statute, but it was a reasonable reading for purposes of constitutional avoidance. Justices Ginsburg, Breyer, Sotomayor, and Kagan joined that portion of the saving construction, giving it five votes, and making that a majority opinion.
Learning Resources operates in something of a mirror fashion. Chief Justice Roberts, as well as Justices Gorsuch and Barrett, found that under the major questions doctrine, the plaintiffs would prevail. While constitutional avoidance in NFIB compelled a saving construction, constitutional avoidance in Learning Resources compelled an anti-saving construction. For a duly-enacted statute, the Court reads the statute to uphold Congress's handiwork. But for a novel executive branch interpretation of an old statute, the Court reads the statute to cut against the President's handiwork. To use Justice Gorsuch's phrasing, "When Congress failed to speak clearly, courts put a thumb on the scale in favor of delegated power. " In other words, Congress puts a thumb on the scale against the executive branch.