By Thomas Ferraro

WASHINGTON (Reuters) - A White House-backed bill to ban workplace discrimination against gays narrowly cleared a Republican procedural roadblock in the U.S. Senate on Monday with the support of a handful of Republicans, just hours after the party's top lawmaker declared his opposition.

On a vote of 61-30, one more than the needed 60, the Democratic-led Senate agreed to begin consideration of the bipartisan bill, with passage likely by the end of this week.

Seven of the 45 Senate Republicans joined 52 Democrats and two independents in voting to move toward passage. All the no votes were cast by Republicans.

The Employment Non-Discrimination Act of 2013 has become the latest example of the ideological struggle in a divided Republican Party.

While an increasing number of Republicans back gay rights, reflecting the sentiment of the country, conservative groups threaten to challenge many of them in next year's elections when a third of the 100-member Senate and the full 435-member House will be up for grabs.

The measure puts Republicans on a political tightrope.

While they face pressure from their party's extreme right, they realize that the gay community, which traditionally votes Democratic, will likely target them if they oppose the bill.

About 5 percent of the voters in the 2012 U.S. presidential election were lesbian, gay or bisexual and 76 percent of them voted for Democratic President Barack Obama, according to a poll commissioned by the Human Rights Campaign and conducted by Greenberg Quinlan Rosner Research.

The survey questioned 1,000 voters who participated in the 2012 election. It had a margin of error of plus or minus 3.1 percentage points.

Once the Senate gives its anticipated approval of the gay-rights bill, the measure will face an uphill climb in the Republican-led House of Representatives where Speaker John Boehner staked out his position in a one-sentence statement.

"The speaker believes this legislation will increase frivolous litigation and cost American jobs, especially small business jobs," said Boehner's press secretary, Michael Steel.

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The statement made it clear that the chances to turn the bill into law before next year's elections were slim and that the legislation may not even come up for a House vote.

Proponents, however, refused to give up hope.

"We feel we have the momentum," said Democratic Senator Tammy Baldwin of Wisconsin, a cosponsor of the bill who last year became the first openly gay person elected to the Senate.

Baldwin said she believed if the bill was brought up for a House vote, it would win bipartisan approval, clearing the way for Obama to sign it into law.

Representative Charlie Dent of Pennsylvania, the leader of a center-right group of about 40 House Republicans, said, "It is my hope that this legislation will be brought to the House floor - allowing the members to vote as they see fit and showing the American people that Congress can work in a bipartisan manner on an important issue of fairness."

White House press secretary Jay Carney said, "The president welcomes the Senate's bipartisan first step towards final passage" of the bill. In a brief statement, Carney made no mention of the House Republican opposition, focusing instead on the Senate cooperation.

RELIGIOUS GROUPS EXEMPTED

The seven Senate Republicans who voted to begin consideration of the bill were Kelly Ayotte of New Hampshire, Susan Collins of Maine, Dean Heller of Nevada, Mark Kirk of Illinois, Rob Portman of Ohio, Orrin Hatch of Utah and Patrick Toomey of Pennsylvania.

The bill would ban workplace discrimination based on sexual orientation or gender identity. Existing federal law already prohibits discrimination based on race, religion, gender, national origin, age, and disability.

Nearly 90 percent of Fortune 500 companies extend workplace protections based on sexual orientation and more than a third on the basis of gender identity, according to supporters of the Senate bill.

Heritage Action, a conservative advocacy group opposed to the bill, warned lawmakers last week that it would include their votes on it in their annual "legislative scorecard." It says the measure would undermine civil liberties, increase government interference in the labor market, and trample on religious liberty.

Although the bill exempts religious groups, the U.S. Conference of Catholic Bishops announced its opposition, in part, because of the measure's support for gay marriage, which the Catholic Church opposes.

The bill is seen as the most significant gay-rights measure to come before Congress since the 2010 repeal of the U.S. military's "don't ask, don't tell" policy on gays serving in the armed forces.

(Reporting by Thomas Ferraro; Editing by Christopher Wilson and Paul Simao)