A decision by Senate Democrats not to add protections for same-sex couples to a landmark immigration reform bill has angered gay rights advocates and put the White House on the defensive over whether President Obama will insist on the provision going forward.

Judiciary Committee Chairman Patrick J. Leahy (D-Vt.) agreed Tuesday night to withdraw an amendment to the immigration legislation that would allow foreign same-sex spouses and partners to apply for visas after it became clear that fellow Democrats would vote against it to preserve Republican support for the bill.

Several key gay rights groups did not accept that rationale, arguing that the issue was a matter of principle and fairness for the estimated 30,000 binational same-sex couples who remain unable to unite in the country. They are currently barred from receiving a spousal visa under the federal Defense of Marriage Act.

“Today it became clear that our so-called ‘friends’ don’t have the courage or the spine to stand up for what’s right,” said Felipe Sousa-Rodriguez, co-director of the advocacy group GetEqual. He added that Democratic lawmakers “are content to buy into the false choice that Republicans created — holding a sorely needed immigration bill hostage in order to cement inequality into law.”

Three Republicans joined the Judiciary Committee’s 10 Democrats in approving the immigration bill 13 to 5 and sent it on to the full Senate, where Leahy could choose to reintroduce the gay rights protections.

White House press secretary Jay Carney said Wednesday that Obama supports the provision, but he declined to say whether the president would insist on it being added to the bill. Obama has told liberals privately that he understands a comprehensive immigration package will not contain all the elements he would like because it requires compromise with Republicans.

The Associated Press, citing two unnamed sources, reported that Obama asked Leahy to hold off on the amendment until the bill emerged from the committee. The White House and Leahy’s office declined to comment on the report.

Obama has “made clear that he supports that and would like to see Congress support that,” Carney said. “He’s also made clear that he doesn’t expect to get everything he wants in this bill.”

Republicans who helped develop the package warned repeatedly that they would withdraw their support if the gay rights provision was added.

Sen. Lindsey O. Graham (R-S.C.), a member of the bipartisan coalition, cited opposition from the Catholic Church.

“It would break the coalition, in my view,” Graham warned Leahy. “You got me on immigration, you don’t have me on marriage. If you want to keep me on immigration, let’s stay on immigration.”

Sen. Charles E. Schumer (D-N.Y.), one of the bill’s lead negotiators, said late Tuesday that Republicans “made it perfectly clear in plain words and on multiple occasions that if this provision is added to the bill they will have no choice but to abandon our collective effort.” He called it “one of the most excruciatingly difficult decisions I’ve had to make in 30-plus years in public office.”

Leahy said he withdrew the amendment “with a heavy heart.”

Human Rights Campaign President Chad Griffin denounced the four Republicans in the bipartisan immigration group — Graham and Sens. John McCain (Ariz.), Marco Rubio (Fla.) and Jeff Flake (Ariz.).

“It is deplorable that a small number of senators have been able to stand in the way of progress for lesbian and gay couples torn apart by discriminatory laws,” Griffin said. “We are extremely disappointed that our allies did not put their anti-LGBT colleagues on the spot and force a vote.”

Some lawmakers hope that the Supreme Court, which is expected to rule on two gay marriage cases next month, will strike down the Defense of Marriage Act, thereby opening the door for same-sex couples to apply for visas.

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