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The Senate on Wednesday cleared a key procedural hurdle to move forward the Respect for Marriage Act, a bill that will codify same-sex marriage into federal law.

The bill earned bipartisan support in a 62-37 vote, with a handful of Republicans voting to move the bill along, giving it enough votes to clear the 60-vote filibuster.

The GOP senators voting in favor were Roy Blunt, Richard Burr, Shelley Moore Capito, Susan Collins, Joni Ernst, Cynthia Lummis, Lisa Murkowski, Rob Portman, Mitt Romney, Dan Sullivan, Thom Tillis and Todd Young.

Senate Majority Leader Chuck Schumer, D-N.Y., spoke from the Senate floor on Wednesday and said the bill is a "simple, narrowly tailored but exceedingly important" measure, "as personal as it gets."

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Ikeita Cantu, left, and her wife Carmen Guzman, of McLean, Va., hold up signs as they celebrate outside of the Supreme Court in Washington, Friday June 26, 2015, after the court declared that same-sex couples have a right to marry anywhere in the US. The couple was married in Canada in 2009 when gay marriage was illegal in Virginia. (AP Photo/Jacquelyn Martin)

Supporters hold signs as they celebrate outside the Supreme Court, June 26, 2015, after the court declared that same-sex couples have a right to marry anywhere in the U.S.

The top senate Democrat reiterated his original intent to introduce the bill for a vote in September, but at the urging of colleagues on both sides of the aisle, he opted to hold off on scheduling a vote to give time for the "bipartisan process to play out."

"Much better to pass this legislation and move equality forward than simply have a show vote, which would bring political reckoning but no real change for the American people," he added.

"If both parties can come together, today could be truly one of the highlights of the year for this body," Schumer said.

The Senate will not sync the bill with the version passed previously by the House of Representatives, and a vote on final passage is expected this week or after the Thanksgiving recess.

Democrat Senate Majority Leader Chuck Schumer

Senate Majority Leader Chuck Schumer of New York (AP Photo/Jacquelyn Martin)

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Susan Collins, R-Maine, a co-author, said the "bill recognizes the unique and extraordinary importance of marriage on an individual and societal level," and she touted the bill’s religious liberty and conscious protections.

Some conservative groups, however, dispute that claim and criticize the bill as "lip service to religious liberty while undermining the First Amendment freedoms available to each of us."

"Right now, government officials across the country—including the Biden administration—argue in court that individuals and religious organizations who love and work with people from all walks of life should face civil and criminal penalties if they don’t abandon their beliefs on this issue," Kristen Waggoner, CEO of Alliance Defending Freedom, said in a statement.

"Make no mistake, this bill will be used by officials and activists to punish and ruin those who do not share the government’s view on marriage," Waggoner said.

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"My job at the end of the day will always be to prioritize getting things passed through this chamber, and marriage equality is too important an issue to risk failure," Schumer said Wednesday.

Rob Portman GOP

Republican Sen. Rob Portman of Ohio is retiring from the Senate at the end of the year. (Al Drago/Pool/AFP via Getty Images)

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"There's every reason under the sun to move forward and begin debating this important legislation," Schumer said.