Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellTrump impeachment trial to begin week of Feb. 8 Democrats float 14th Amendment to bar Trump from office Biden signals he's willing to delay Trump trial MORE (R-Ky) said there's little lawmakers can do to overturn a Supreme Court ruling allowing same-sex marriages in every state, suggesting any further action will rest largely with the courts. 
"I don't think so. I think the courts have pretty well spoken. We'll be taking a look at whether or not religious liberty needs to be enhanced by statue," the Republican leader told WDRB, a local Kentucky TV station, on Tuesday evening, when asked if there was anything Congress could do to reverse the court's decision.
McConnell added, "What I worry about at this point is the potential problems with regard to religious liberty. … There's a possibility of legislation, but I think most of this is going to be in the courts."
His comments come in the wake of the Supreme Court's ruling that legalized same-sex marriage in all 50 states. 
McConnell's Republican colleagues quickly vowed to try to protect religious freedom in light of last week's decision. 
Sen. Mike LeeMichael (Mike) Shumway LeeOvernight Defense: Austin takes helm at Pentagon | COVID-19 briefing part of Day 1 agenda | Outrage over images of National Guard troops in parking garage Austin sworn in as nation's first Black Pentagon chief The Hill's 12:30 Report: Next steps in the Trump impeachment MORE (R-Utah) vowed to get his legislation, the First Amendment Defense Act, passed. The Utah Republican said the bill would "prevent the federal government from discriminating against anyone who believes that marriage is a union between one man and one woman."  
But McConnell shot down his effort, saying it wouldn't make it through Congress.
"It isn't going to pass. It's one thing to talk about a constitutional amendment," he said. "We've only done that 27 times in the history of our country. It's not going to pass." 
McConnell and Cruz were part of a group of six senators who signed on to an amicus brief calling on the court to protect state bans on same-sex marriage. 
"I've always felt that marriage was between one man and one woman," he said Tuesday night. "The Supreme Court has held otherwise, that's the law of the land."