A supporter of LGBTQ rights holds up an "equality flag" on Capitol Hill. (Jacquelyn Martin/AP)

This week, Democrats will launch a new effort to pass the Equality Act, a sweeping bill that would ban discrimination against the LGTBQ community.

“LGBTQ people in 30 states still do not have clear protections from discrimination in employment, housing and public spaces,” tweeted Rep. Sheila Jackson Lee (D-Tex).

"We want to live in a country that, you know, judges people based on their performance and their character, and so we need to pass the Equality Act at the federal level,” Sen. Tammy Baldwin (D-Wis.), the first openly LGBTQ person elected to the Senate, told CNBC.

The measure, which would update the Civil Rights Act, has been introduced before. In 2015, it couldn’t get through the Republican-controlled Congress.

This time, though, there’s a small chance the measure could clear the Democratic-controlled House and the Republican-led Senate. With public opinion on LGBTQ issues changing, conservative lawmakers may have a difficult time presenting a united opposition to the legislation.

For starters, the measure is popular. The majority of Americans — more than 71 percent — support laws like the Equality Act, according to a recent survey by PRRI.

Additionally, businesses have come out in favor of the measure. A growing number of high-profile firms have signed on to the Business Coalition for the Equality Act. Mark King heads diversity and inclusion at the Kellogg Co., one of more than 160 businesses in support of the Equality Act. He said in a statement:

“Supporting the Equality Act demonstrates our continued commitment to creating an environment in which all employees are included, treated with dignity and respect, and are empowered to achieve their full potential.”

Companies like Apple, Wells-Fargo, Twitter and Pfizer have also signaled their support.

But the legislation is unpopular with constituencies that tend to back the Republican Party, and they are pushing back. According to that PRRI poll, nearly two-thirds of Republicans say small-business owners should be allowed to refuse service to LGBTQ people. More than 6 in 10 white evangelicals agree.

Religious conservatives have attacked the act as a potential violation of religious rights. Andrew Walker, a senior fellow at the Ethics and Religious Liberty Commission, wrote in the Gospel Coalition that the bill is a threat to the religious liberty of social conservatives. He wrote:

The bill represents the most invasive threat to religious liberty ever proposed in America. Given that it touches areas of education, public accommodation, employment, and federal funding, were it to pass, its sweeping effects on religious liberty, free speech, and freedom of conscience would be both historic and also chilling.

The Equality Act must be opposed. Any Christian legislator or conservative legislator who understands the vital urgency of religious liberty must oppose it.

All this could put some more moderate Republicans, particularly those representing states that lean Democratic, in a tough position.

That is, of course, if Senate Majority Leader Mitch McConnell (R-Ky.) decides to bring the bill to the floor at all. He has not committed to doing so. Meanwhile, most GOP lawmakers have avoided taking a position on the legislation, surely mindful of the ramifications of doing so. And expressing opposition to the act is quite risky for those conservatives in more purple districts. And conservatives supporting the legislation could expose themselves to tough primaries, facing motivated Republican voters who have in some ways become increasingly conservative in the Trump era.