The new legislation will bring the Alpine nation into line with much of Western Europe and can take effect on July 1, 2022.
The Republican congresswoman, whose sister is married to a woman, said her previous views were "misguided."
Justices Clarence Thomas, Samuel Alito and Neil Gorsuch said they would have agreed to hear the case and review the decision.
Phyllis Lyon and Del Martin were wed in 2004 and again in 2008, when marriage equality became the law of the land in California.
"Why not get married, why not fall in love and have all the happiness that everybody else is entitled to?" the CNN anchor asked on the "Tamron Hall Show."
Priests in Germany and other parts of Northern Europe have been blessing gay couples in committed relationships for years.
The "Rocket Man" used his relationship milestone to acknowledge the millions of queer people who continue to face discrimination.
The conservative justice criticized science-backed COVID-19 restrictions and condemned the Supreme Court's 2015 decision to legalize same-sex marriage.
Nearly 62% of voters backed an amendment ensuring protections for married LGBTQ couples even if marriage equality gets overturned at the federal level.
Before becoming pope, Francis supported extending legal protections to gay couples in Argentina. Those comments are now putting the Vatican in a bind.