Congress can begin to fix the decision by approving a Constitutional amendment proposal and sending it to the States for ratification.
Short of disregarding the Supreme Court’s decision - - which would undermine the Court’s very legitimacy - - Congress cannot overrule the Supreme Court’s interpretation of the Constitution without moving to amend the Constitution. That is why the Constitutional amendment process has been necessary to correct egregiously wrong decisions of the Supreme Court, from deciding that African Americans, “whether emancipated or not,” are not citizens and “had no rights which the white man is bound to respect” (Dred Scott v. Sandford, 60 U.S. 393 (1856)) to deciding that even if women were citizens under the 14th Amendment, they had no right to vote because the Constitution, according to the Court, did not guarantee the right to vote as among the fundamental rights, privileges or immunities of citizenship (Minor v. Happersett, 88 U.S. 162 (1874)).
Congress and the States can and should take many steps short of amendment to make elections more fair and to improve the likelihood that legislatures will reflect the will of the people, from approving public funding mechanisms to eliminating barriers to registration and voting. None of these will be sufficient, however, if we do not correct the Court’s perversion of the First Amendment and the Constitution into a corporate protection device.