I would also assume the government defends any federal law on commerce clause grounds.
Justice Thomas has written extensively about his views of the commerce clause, and I think he would reject any such arguments except as applied to transactions that actually cross state lines. See his concurrence in United States v. Lopez, 514 U.S. 549 (1995) and his dissent in Gonzalez v. Raich, 545 U.S. 1 (2005).
Perhaps most relevant was the case Gonzales v. Carhart, 550 U.S. 124 (2007), where the Court tackled the federal partial-birth abortion ban. It was taken as given that Congress enacted the law under its commerce clause. The law was written to that extent, “[a]ny physician who, in or affecting interstate or foreign commerce, knowingly performs a partial-birth abortion…”
Justices Alito, Thomas, and Chief Justice Roberts were on the Court at the time. Justice Thomas had also been on the court for the prequel, Stenberg v. Carhart, 530 U.S. 914 (2000), which involved the same physician challenging a similar state law.
Justice Kennedy wrote the Gonzalez opinion which Chief Justice Roberts, Justice Thomas, and Justice Alito joined. You can see the commerce power was mentioned only in passing:
A zero tolerance policy would strike down legitimate abortion regulations, like the present one, if some part of the medical community were disinclined to follow the proscription. This is too exacting a standard to impose on the legislative power, exercised in this instance under the Commerce Clause, to regulate the medical profession. Considerations of marginal safety, including the balance of risks, are within the legislative competence when the regulation is rational and in pursuit of legitimate ends. When standard medical options are available, mere convenience does not suffice to displace them; and if some procedures have different risks than others, it does not follow that the State is altogether barred from imposing reasonable regulations. The Act is not invalid on its face where there is uncertainty over whether the barred procedure is ever necessary to preserve a woman’s health, given the availability of other abortion procedures that are considered to be safe alternatives.
Justice Thomas also joined Justice Scalia’s concurrence, which in relevant part said:
I also note that whether the Partial-Birth Abortion Ban Act of 2003 constitutes a permissible exercise of Congress’ power under the Commerce Clause is not before the Court. The parties did not raise or brief that issue; it is outside the question presented; and the lower courts did not address it. See Cutter v. Wilkinson, 544 U.S. 709, 727, n. 2 (2005) (Thomas, J., concurring).
~Max