SAN FRANCISCO — Same-sex marriage proponents and the city of San Francisco, riding a wave of political popularity to the U.S. Supreme Court, may have hit a legal roadblock, as four of the court’s five conservative justices — including the usual swing vote, Anthony Kennedy — sounded hostile Tuesday to a Ninth Circuit decision striking down Proposition 8.

What’s more, the questioning mostly ignored the 80 detailed factual findings U.S. District Judge Vaughn Walker made at trial in the case of Hollingsworth v. Perry — findings that same-sex marriage supporters hoped would make it more difficult for the Supreme Court to rule against them.