General Assembly Democrats launched a legislative campaign Monday to expand gay rights, hoping to take advantage of their party’s recent sweep of statewide offices as well as changing public opinion on the issue across Virginia and the nation.

The effort, which includes legislation on discrimination and marriage recognition, comes days after newly inaugurated Gov. Terry McAuliffe (D) promised to champion equality for gay couples.

It also comes at a time of recalibration for Republicans, who for years successfully moved the state’s laws to the right on gay rights and abortion. Stung on those issues in recent elections, some in the GOP are trying to avoid the topics, as Democrats aim to force votes on policies on which they think their opponents are increasingly out of step with the public.

Democratic lawmakers took up the cause at a morning news conference, backing measures repealing the state’s constitutional ban on gay marriage, banning discrimination in housing, allowing civil unions, recognizing same-sex marriages from other states and banning gay conversion therapy.

“Our marriage laws are becoming more and more antiquated every day,” said Sen. Adam Ebbin (D-Alexandria), the first openly gay state senator. “Virginia needs to be a place . . . where same-sex couples aren’t treated like second-class citizens.”

In his inaugural address Saturday, McAuliffe pledged to work to ensure that opportunities are equal for all of Virginia’s children — “no matter whom you love.” He said the state must “ensure that someone can’t lose a job simply because they are gay.” And after the ceremony ended, he signed an executive order banning discrimination against gay and transgender employees in state government.

With the state House still dominated by Republicans and the Senate divided, it appears unlikely that Democrats will be able to roll back some of the more controversial measures passed in recent years, notably the constitutional amendment banning gay marriage. Even trying, however, could put Republicans in the vulnerable position of having to defend politically damaging positions.

Republicans, meanwhile, are calling for a moratorium on the topic.

“We are disappointed General Assembly Democrats would choose to make a divisive social issue the centerpiece of their legislative agenda,” said Matt Moran, a spokesman for the House Republican caucus. “Our focus should be on creating jobs and improving our schools. That’s what the people of Virginia want us to work on.”

Victoria Cobb, president of the socially conservative Family Foundation, likewise argued that “instead of focusing on jobs and the economy, liberals in Virginia have introduced nearly 20 bills dealing with sex and abortion.”

Democrats said that gay rights is a business issue as well as a moral one, because gay workers or gay-friendly businesses might be lured away by other states that offer more protections.

The Northern Virginia Technology Council, a prominent business group that endorsed former attorney general Ken Cuccinelli II, the Republican nominee for governor last fall, backed that view in a statement applauding McAuliffe’s executive order as helpful for the “recruitment and retention of the skilled workers who are critical to the growth of our innovation economy.”

Rep. David B. Albo (R-Fairfax), who supports anti-discrimination legislation, said that a cease-fire is a nice idea but unlikely. “It’s not my cup of tea,” he said about social issues in general. “But some people are preoccupied with them, and everybody has the right to file a bill.”

In fact, in a sign of shifting public opinion, two Republicans have filed pro-gay-rights legislation in the House. Two of the bills echo Democratic legislation barring discrimination in public employment and housing. Another allows for a non-spousal partner to become a child’s adoptive parent.

“It’s just the evolution of myself,” said Del. Ronald A. Villanueva (R-Virginia Beach) of his anti-discrimination bill. On the Republican side, he said, “there are some folks that are supportive and some that argue some of the older arguments that you see. Hopefully it will help push the discussion further.”

No lawmaker has yet attempted a repeal of a 2012 law allowing private adoption agencies taking state money to turn away parents based on sexual orientation.

A clear majority of Virginians, 56 percent, now support making gay marriage legal, a near-mirror-image of the 57 percent who voted for the ban in 2006. That majority includes 40 percent of Republicans, compared with the 15 percent who felt that way when the constitutional amendment was passed.

But just as in Congress, where federal anti-discrimination legislation has passed the Senate, Republicans control the other chamber. Even if Democrats were able to pass some of their initiatives in the evenly divided Senate, the measures would almost certainly die in the House, where many Republicans won’t back an expansion of gay rights even if they aren’t seeking to narrow them.

“I don’t think there’s a huge downside” for McAuliffe in putting his support behind these measures despite the “uphill battle” in the General Assembly, said Bob Holsworth, a longtime Virginia political analyst. “He can put out some markers. Even if he doesn’t get all that he wants, given the evolving nature of this issue, he may by the end of his term.”

Republican leaders have worked this year to downplay social issues, even snagging House Bill 1, which has regularly been taken in past years by conservative Del. Robert G. Marshall (R-Prince William) for a proposed abortion restriction.

And Marshall is the only Republican to file a bill this session that would restrict gay rights — a proposal that would ban same-sex couples from filing taxes jointly.

It’s a pressing issue for gay couples who have been legally married elsewhere. In one of his final acts as attorney general, Cuccinelli issued an opinion backing a Virginia Department of Taxation ruling that these couples cannot have joint tax status on their Virginia returns.

Newly installed Attorney General Mark R. Herring (D) will “be looking closely” at that opinion, a spokeswoman said. The Virginia ACLU has asked McAuliffe for an additional executive order allowing same-sex couples to file jointly but has not yet received a response.

By most accounts, efforts to repeal the 2006 marriage ban has virtually no hope of passage this session. Del. Mark Cole (R-Spotsylvania), chairman of the committee that considers constitutional amendments, has said that none will be considered this year because Virginia law requires that they be voted on both before and after an election.

Courts may ultimately decide the issue: two federal lawsuits against Virginia’s gay marriage ban and refusal to recognize same-sex marriages from other states will be heard this year.

But Democrats are moving forward with legislation to repeal the ban.

“It very well may not be until 2015 when the amendment will come up,” Sen. Donald McEachin (D-Henrico) said Monday. “But we go forward nonetheless.”