WASHINGTON — The Senate prepared to push a major, anti-bias gay rights bill past a first, big hurdle Monday, a clear sign of Americans’ greater acceptance of homosexuality nearly two decades after lawmakers narrowly rejected discrimination legislation.

The legislation that would prohibit workplace discrimination against gay, bisexual and transgender Americans could win Senate passage by week’s end, but its prospects in the Republican-majority House are dimmer.

A stark reminder of the nation’s changing views, lingering resistance to homosexuality and the political implications resonated in Maine, as six-term Democratic Rep. Mike Michaud, who is running for governor, said he was gay and questioned whether it still mattered to voters.

Hours before Monday’s vote, President Barack Obama issued a fresh plea for passage of the Employment Non-Discrimination Act, the first significant gay rights bill since Congress lifted the ban on gays serving openly in the military nearly three years ago.

“Americans ought to be judged by one thing only in their workplaces: their ability to get their jobs done,” the president said in a message written for Huffingtonpost.com. “Does it make a difference if the firefighter who rescues you is gay — or the accountant who does your taxes or the mechanic who fixes your car?”

All 55 members of the Democratic majority and at least five Republicans were expected to vote to proceed with the bill, giving Majority Leader Harry Reid, D-Nev., the 60 votes necessary. Reid’s Republican colleague in Nevada, Dean Heller, announced his support on Monday, saying that the measure “raises the federal standards to match what we have come to expect in Nevada, which is that discrimination must not be tolerated under any circumstance.”

Opening Senate debate, Reid quoted slain gay rights leader Harvey Milk, who argued that freedom and individual rights shouldn’t hinge on political deals and opinion polls.

The law, Reid said, would ensure that “all Americans regardless of where they live can go to work unafraid to be who they are.” Sen. Tom Harkin, D-Iowa, called the measure another step forward in the country’s progress.

The administration, in a strong statement of support, said passage of the bill was long overdue.

Current federal law prohibits discrimination on the basis of sex, race and national origin. But it doesn’t stop an employer from firing or refusing to hire workers because they are gay, lesbian, bisexual or transgender. The bill would bar employers with 15 or more workers from using a person’s sexual orientation or gender identity as the basis for making employment decisions, including hiring, firing, compensation or promotion.

Possible passage of the bill by week’s end would cap a 17-year quest to secure Senate support for the anti-bias measure that failed by one vote in 1996, the same year Congress passed and President Bill Clinton signed the Defense of Marriage Act. That law required the federal government to refuse to recognize same-sex marriages.

In 1996, Sen. Orrin Hatch of Utah voted against the bill. Earlier this year, he was one of several Republicans to back the measure in committee along with Sen. Lisa Murkowksi of Alaska. Seventeen years ago, Murkowski’s father Frank —then the state’s senator — voted against the bill.

Today Americans have shown increasing support for same-sex marriage, now legal in 14 states and the District of Columbia. The Supreme Court in June affirmed gay marriage and granted federal benefits to legally married same-sex couples.

Meanwhile, in Maine, Michaud wrote about his homosexuality.

“That may seem like a big announcement to some people. For me, it’s just a part of who I am, as much as being a third-generation mill worker or a lifelong Mainer. One thing I do know is that it has nothing to do with my ability to lead the state of Maine,” Michaud wrote in an op-ed article.

The anti-discrimination bill faces strong opposition from conservative groups — Heritage Action and the Faith and Freedom Coalition said the vote will be part of their legislative scorecard on lawmakers. More to its immediate prospects, the legislation is opposed by Speaker John Boehner, R-Ohio, and it’s unclear whether the House will even vote on the measure.

Reiterating Boehner’s longstanding opposition, spokesman Michael Steel said Monday that Boehner “believes this legislation will increase frivolous litigation and cost American jobs, especially small business jobs.”

Besides Heller, four other Republican senators are backing the legislation — Susan Collins of Maine, Mark Kirk of Illinois, Hatch and Murkowski — and proponents expect a few others to support it.

Chad Griffin, president of the Human Rights Campaign, the largest gay and lesbian advocacy group, contrasted Heller’s backing with Boehner’s opposition.

“The speaker, of all people, should certainly know what it’s like to go to work every day afraid of being fired,” Griffin said, a reference to the unsuccessful, tea party-backed challenge to Boehner earlier this year.