Sen. Mike Lee, R-Utah, on Wednesday criticized the Respect for Marriage Act, legislation that would codify same-sex marriage into federal law, arguing the bill has inadequate protections for religious liberty. 

Lee shared a statement from Roger Severino, vice president of domestic policy at the Heritage Foundation, who asserted the bipartisan bill would be "used as a cudgel against those who believe in the reality of marriage as between a man and a woman." 

"Roger Severino is right: No American should face legal threats for holding sincere religious beliefs or convictions," Lee wrote on Twitter. "The bill before the Senate presents such a threat, and offers protections for religious freedom that can only be described as severely anemic." 

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There is bipartisan support for codifying same-sex marriage, which the U.S. Supreme Court legalized in 2015 with the landmark Obergefell v. Hodges decision. Senate Majority Leader Chuck Schumer, D-N.Y., has scheduled a procedural vote on The Respect for Marriage Act for Wednesday and the bill is expected to pass later this week, or possibly after Thanksgiving. 

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Bill sponsors Sens. Rob Portman, R-Ohio, Tammy Baldwin, D-Wis., Susan Collins, R-Maine, Kyrsten Sinema, D-Ariz., and Thom Tillis, R-N.C., released a joint statement Monday saying that through "bipartisan collaboration, we’ve crafted commonsense language that respects religious liberty and Americans’ diverse beliefs, while upholding our view that marriage embodies the highest ideals of love, devotion, and family."

Lee noted that he had offered an amendment that would strengthen religious liberty protections by preventing the government from removing tax-exempt status for religious organizations based on their convictions on marriage, but said the sponsors "refused even to consider that." 

Fox News' Brianna Herilhy and Chad Pergram contributed to this report.