"I believe in my heart of hearts that what you're doing is the right and just thing," said Sen. Richard Durbin, D-Ill. "But I believe this is the wrong moment, that this is the wrong bill."
Sens. Chuck Schumer, D-N.Y., and Al Franken, D-Minn., added their voices, and Leahy announced that, "with a heavy heart," he would withdraw his amendment.
Gay rights groups voiced outrage, and the issue is certain to re-emerge when the full Senate debates the legislation. But it is doubtful that sponsors can command the 60 votes that will be needed to make it part of the legislation.
In the hours leading to a final vote, the panel also agreed to a last-minute compromise covering an increase in the visa program for high-tech workers, a deal that brought Hatch over to the ranks of supporters.
Under the bill, the number of highly skilled workers admitted to the country would increase greatly, but there were also protections aimed at ensuring U.S. workers get the first shot at jobs, and high-tech companies objected to some of those.
Under the deal, companies in which foreign labor accounts for at least 15 percent of the skilled workforce would be subjected to tighter conditions than businesses less dependent on H-1B visa holders, and requirements on recruiting and hiring and firing of U.S. workers would be relaxed.
In defeat, opponents said they, too, wanted to overhaul immigration law, but not the way that drafters of the legislation had done.
Sen. Charles Grassley, R-Iowa, recalled that he had voted to give "amnesty" to those in the country illegally in 1986, the last time Congress passed major immigration legislation. He said that bill, like the current one, promised to crack down on illegal immigration, but said it had failed to do so.
"No one disputes that this bill is legalization first, enforcement later. And that's just unacceptable to me and to the American people," he said.
AP White House Correspondent Julie Pace contributed to this report.
- Co-pilot who reportedly crashed plane into...
- 'A marvellous work and a wonder': A look back...
- Rep. Trey Gowdy: Hillary Clinton wiped email...
- Senate's Harry Reid announces he won't seek...
- Sen. Harry Reid's retirement recalls his...
- The Latest: Hospital says it evaluated...
- 'Downton Abbey' to end after upcoming 6th season
- Therapists share healing powers of horses at...
- 'A marvellous work and a wonder': A... 62
- 'Maternal feminists' defend motherhood... 53
- Texas Sen. Ted Cruz targets... 44
- Rep. Trey Gowdy: Hillary Clinton wiped... 38
- Senate's Harry Reid announces he won't... 33
- Alone at controls, Germanwings co-pilot... 27
- Sen. Mike Lee not ready to endorse Ted... 18
- Preparing for 2016 campaign, Hillary... 17