Just because the federal Constitution does not recognize a fundamental privacy interest which covers obtaining an abortion does not mean any legislative body has the power to pass a law offending that interest.
State legislatures are usually confined by state constitutions. While many state legislatures can and have banned abortions within their states, some state constitutions limit the power of the state legislature by protecting abortion access. The federal Congress only possesses limited legislative powers, and I think a national abortion ban is beyond Congress’s powers, not because the Constitution recognizes a fundamental privacy right to abortion, but because I don’t see how a national abortion ban falls within the enumerated powers of Congress.
~Max