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Bipartisan Senate group says they are 'confident' they have the votes necessary to codify same-sex marriage

(CNN) The bipartisan group working on legislation to codify same-sex marriage has the votes needed for the bill to pass and is urging leadership to put it on the floor for a vote as soon as possible, multiple sources told CNN.

The bipartisan group, which includes GOP Sen. Rob Portman of Ohio, Democratic Sen. Tammy Baldwin of Wisconsin, GOP Sen. Susan Collins of Maine, Democratic Sen. Kyrsten Sinema of Arizona, and GOP Sen. Thom Tillis of North Carolina, said in a statement Monday that they "look forward to this legislation coming to the floor."

"Through bipartisan collaboration, we've crafted commonsense language to confirm that this legislation fully respects and protects Americans' religious liberties and diverse beliefs, while leaving intact the core mission of the legislation to protect marriage equality," the senators said in the statement. "We look forward to this legislation coming to the floor and are confident that this amendment has helped earn the broad, bipartisan support needed to pass our commonsense legislation into law."

Democrats were hoping to pass the legislation during the lame-duck session but as of Monday morning it was unclear when that would happen.

Senate Majority Leader Chuck Schumer on Monday took procedural steps related to the same-sex marriage bill, setting up the first test vote for Wednesday.

"I'm going to set up the first procedural vote on legislation that will codify marriage equality into law. Members should expect the first vote on Wednesday," he said.

"No American should ever be discriminated against because of who they love and passing this bill would secure much needed safeguards into federal law," Schumer said.

In early September, Schumer vowed to bring the bill to the floor for a vote in "the coming weeks."

"The Senate will hold a vote on the Respect for Marriage Act in the coming weeks, so that no American is discriminated against because of whom they love," he said, adding that he hopes enough GOP senators join Democrats in support of passage.

But the bill's supporters said in September that more time was needed to negotiate the issue with Republicans -- and sought to delay any vote in the Senate until after the November midterm elections, which Schumer agreed to.

The bill will need at least 10 GOP Senate votes to overcome a filibuster and advance the legislation toward final passage.

This story has been updated with additional developments Monday.