In the aftermath of the Dobbs decision, some conservatives are talking about passing a national ban on abortion. But I don't think they can do that.
The Constitution gives Congress the power to enact laws concerning certain enumerated topics: bankruptcy, immigration, terrorism, espionage, taxes, counterfeiting, and so on. Generally speaking, however, criminal law is reserved to the states. The exception is for criminal acts that specifically implicate federal interests: murdering a federal officer, for example, or robbing someone on federal property.
So could Congress enact a national ban on abortion? If they can't even pass broad laws against murder or assault, it seems unlikely. This is one reason that current federal abortion law is extremely constrained: The Hyde Amendment prohibits the use of federal funds to pay for abortions and the 2004 Unborn Victims of Violence Act applies to a subset of cases where the underlying crime is a federal offense. Broader applications might be possible using Congress's interstate commerce power—mailing pills across state lines, for example—but that's a long shot.
It's especially a long shot since Sam Alito spent about 20,000 words in Dobbs (a) talking nonstop about state law and its history, (b) giving no indication that the Constitution provides Congress any power over abortion, and (c) specifically denying that the 14th Amendment federalizes either the right or crime of abortion. As for interstate commerce, the current Court has been at pains to rein in the interstate commerce power, not expand it.
This is mere logic, of course, and conservatives on the Supreme Court can just ignore it if they want. Still, there are limits, even for these folks. They just signed onto a huge decision that, in every possible way, supports the idea that abortion is strictly a state issue, not a federal one. They'd have a hard time changing that any time soon.
POSTSCRIPT: Unfortunately, this same reasoning applies to any attempt to "codify Roe." Maybe I'm wrong, but I don't think Congress can do this either. And if they did, the Supreme Court would obviously have no problem striking it down since that would be consistent with the text of Dobbs.