* Judiciary Committee approved easing high-tech visa plan
* Bill now heads to Senate floor for June debate
* Obama says legislation consistent with his goals
WASHINGTON, May 21 (Reuters) - A U.S. Senate panel on Tuesday approved legislation to give millions of illegal immigrants a path to citizenship, setting up a spirited debate next month in the full Senate over the biggest changes in immigration policy in a generation.
President Barack Obama, who has made enactment of an immigration bill one of his top priorities for this year, praised the Senate Judiciary Committee's action, saying the bill was consistent with the goals he has expressed.
"I encourage the full Senate to bring this bipartisan bill to the floor at the earliest possible opportunity and remain hopeful that the amendment process will lead to further improvements," Obama said in a statement released by the White House.
By a vote of 13-5, the Senate panel approved the bill that would put 11 million illegal residents on a 13-year path to citizenship while further strengthening security along the southwestern border with Mexico, long a sieve for illegal crossings into the United States.
The vote followed the committee's decision to embrace a Republican move to ease restrictions on high-tech U.S. companies that want to hire more skilled workers from countries like India and China.
In a dramatic move before the vote, Senate Judiciary Committee Chairman Patrick Leahy, a Democrat from Vermont, withdrew an amendment to give people the right to sponsor same-sex partners who are foreigners for permanent legal status.
Leahy's colleagues on the committee - Republicans and Democrats - warned that the amendment would kill the legislation in Congress. Democrats generally favor providing equal treatment for heterosexual and homosexual couples, while many Republicans oppose doing so.
"I'm committed to ending that discrimination," Leahy said before withdrawing the amendment.
"Democrats should be ashamed of themselves for not defending LGBT (lesbian, gay, bisexual, transgender) families against the scapegoating of their Republican colleagues," said Rachel Tiven, executive director of Immigration Equality, a gay rights group.
Republican Senator Orrin Hatch of Utah said the changes made to visa rules governing high-skilled workers, which he had demanded on behalf of the U.S. technology industry, were the price of his support for the bill when the committee voted. Hatch voted for the bill.
In another encouraging sign for the legislation, Senate Republican Leader Mitch McConnell said he will not block the measure from coming to the floor for a full debate.
McConnell of Kentucky did not say how he ultimately would vote on the bill, but he told reporters that the bipartisan measure "made a substantial contribution to moving the issue forward."
All of the core elements of the legislation have been maintained after five long work sessions by the committee. Furthermore, some border security provisions critical to conservatives and border-state members of Congress have been strengthened.
Frank Sharry, executive director of the pro-immigration reform group America's Voice, said the bill was now "battle-tested" and was emerging with more Republican support than when the Senate panel began work on it this month.
"It's remarkable. You have a dysfunctional Congress, where both parties have been at war with each other, working together on a bipartisan basis on a controversial issue and making tremendous progress," Sharry told Reuters.
That bipartisanship may have been fostered, at least in part, by the Nov. 6 presidential election in which Obama vowed to get an immigration bill through Congress as his Republican challenger, Mitt Romney, urged undocumented immigrants to simply "self-deport."
Romney won less than 30 percent of the Hispanic-American vote, spurring Republican party leaders to quickly pivot and call for passing comprehensive immigration legislation.
Some of the most conservative Republicans on the Senate panel, however, persisted in their attempts to significantly change the bill ahead of Tuesday's vote.
One of the sharpest exchanges came when Republican Senator Ted Cruz of Texas offered amendments to kill the pathway to citizenship for the 11 million and to permanently deny some of them federal benefits aimed at low-income people.
The path, Cruz argued, "will serve only to encourage yet more illegal immigration. It will not solve the problem."
Democratic Senator Dick Durbin of Illinois, noting the Texan's amendments would deny education, nutrition and health benefits for low-income people who are winning legal status and ultimately citizenship, said Cruz's message to undocumented immigrants was, "We don't want you. You can't be part of the future of this nation."
"What kind of America are you thinking of here, Senator Cruz?" Durbin asked.
Meanwhile, Hatch warned that even with his victory on visa rules for high-tech foreign workers, his ultimate support for the bill would hinge on a set of controversial amendments that he would propose during the full Senate debate.
Those are thought to be aimed mostly at preventing illegal immigrants who move to legal status from getting certain government programs, including Social Security retirement benefits and tax credits for children and families with low incomes. Republicans also want to prevent newly-legalized residents from getting government healthcare benefits.
Denying healthcare benefits under "Obamacare," the president's sweeping 2010 healthcare restructuring, is a major sticking point in the Republican-controlled House of Representatives, where a bipartisan group of eight lawmakers were meeting on Tuesday to cobble together their own immigration bill.
The immigration bill currently requires all companies that hire employees on H-1B visas for specialized workers to advertise job openings on a government website and offer them first to any qualified Americans.
One of Hatch's proposals, worked out in a deal with New York Democratic Senator Charles Schumer, would require only companies defined as "H-1B dependent" to give Americans the first shot at jobs. It was strongly opposed by the AFL-CIO labor organization.
The Schumer-Hatch deal also changes the definition of an H-1B-dependent company, which currently is any firm where more than 15 percent of the workforce are on high-skilled work visas. Under the amendment, it would apply only where more than 15 percent of workers in a specific occupation within the company are using the H-1B visa.
Steve Case, the co-founder and former chairman and CEO of AOL, called the deal a major breakthrough. A coalition of tech groups that had been lobbying for the changes promptly issued a letter in support of the bill. One source said tech groups agreed that they would enthusiastically support the bill if the changes were made.
But AFL-CIO President Richard Trumka called the changes "unambiguous attacks on American workers." He added, "American corporations could fire American workers in order to bring in H-1B visa holders at lower wages."