Warning of Texas-style laws nationwide, the party believes it can use the issue to turn out suburban women in the Virginia governor’s race this fall and the 2022 midterms.VIRGINIA BEACH — Kenzie Smith is “not big into politics,” she said, and while she votes faithfully in presidential elections, for Democrats, she is less interested in off-year races, such as those seven weeks away in Virginia for governor and the legislature.But the recent news that the Supreme Court had allowed Texas to ban most abortions after about six weeks of pregnancy, with no exceptions for rape or incest, grabbed her attention.The fear that such a restrictive law, which she called “insane,” could come to Virginia if Republicans take power has sharpened her desire to turn out on Election Day. “If there are laws like what’s going on in Texas coming here, I’d absolutely be motivated to go to the polls over that,” said Ms. Smith, 33, a marketing consultant.The Supreme Court’s decision on Sept. 1 to let Texas enact the country’s most restrictive abortion law came as a grievous blow to abortion rights advocates, a long-sought victory for abortion opponents and, for Democrats, a potential political opportunity.As the party mobilizes for next year’s midterms, its first big test on the issue will come in the Virginia elections this fall. Democrats are hoping to win a tight governor’s race and keep control of the legislature in a state that has moved rapidly to the left. Former Gov. Terry McAuliffe, a Democrat who is running for his old office, has repeatedly promised to be a “brick wall” against anti-abortion measures, and has played up his defense of abortion rights at a debate last week, on the campaign trail and in fund-raising appeals.Democrats in Virginia and beyond are focusing in particular on suburban women, who played a large role in electing President Biden, but whose broader loyalty to his party is not assured. With Republicans smelling blood in next year’s midterm elections as Mr. Biden’s approval ratings slip and the economy faces a potential stall over the lingering pandemic, Democrats are looking for issues like abortion to overcome their voters’ complacency now that Donald J. Trump is gone from office.In more than two dozen interviews in the politically divided city of Virginia Beach, the largest in the state but essentially a patchwork of suburban neighborhoods, Democratic-leaning and independent female voters expressed fear and outrage over the Supreme Court’s green light for the Texas law. Many said it intensified their desire to elect Democrats, although historically, single issues have not driven turnout waves; candidate personalities and the overall economy have.Even a number of women who said they favored Republicans noted that they also supported abortion rights — which may explain why G.O.P. candidates in Virginia have played down the issue, scrubbing anti-abortion comments from campaign websites and walking back some remarks.In a debate on Thursday between candidates for governor, Glenn Youngkin, the Republican, said, “I would not sign the Texas bill today.” But he dodged when asked if he would sign a six-week abortion ban with exceptions for rape and incest. He affirmed that he supported a “pain-threshold bill,” which generally outlaws abortion after 20 weeks.Mr. McAuliffe said he was “terrified” that “the Trump Supreme Court” could overturn Roe v. Wade, the 1973 landmark decision granting a constitutional right to an abortion. He said he supported “a woman’s right to make her own decision to a second trimester.” He misleadingly said that Mr. Youngkin “wants to ban abortions.”Early in the campaign, a liberal activist recorded Mr. Youngkin saying that he had to play down his anti-abortion views to win over independents, but that if he were elected and Republicans took the House of Delegates, he would start “going on offense.” The McAuliffe campaign turned the recording into an attack ad.Ellen Robinson was “horrified” by the Texas law.Carlos Bernate for The New York TimesKathleen Moran said the Supreme Court’s decision on the Texas law “scared” her.Carlos Bernate for The New York TimesRepublicans portray Mr. McAuliffe as favoring abortions up to the moment of birth, trying to tie him to a failed 2019 bill in the legislature that would have loosened some restrictions on late-term abortions. Virginia law permits abortions in the third trimester if a woman’s life is in danger.Polling on abortion shows that Americans’ attitudes have remained stable for decades, with a majority of around 60 percent saying abortion should be legal in all or most cases. In Virginia, slightly fewer people, 55 percent, agree, according to the Pew Research Center.However, in a contradiction that illustrates the moral complexities of the issue, national polls also show that majorities favor abortion restrictions that are impermissible under Roe, such as outlawing second-trimester abortions in most cases.A Washington Post-Schar School poll of Virginia conducted this month, after the Supreme Court cleared the way for the Texas law, found that abortion ranked low among voters’ concerns, with only 9 percent saying that it was their most important issue in the governor’s race.The starkness of the Texas decision — and the prospect that the Supreme Court could overturn Roe next year in a case involving a 15-week abortion ban in Mississippi — has sharpened the issue.Virginia Beach presents a test case of the fraught abortion issue on the front lines of America’s shifting electoral landscape. The large population of military families has long lent a conservative cast to local politics, but last year the city voted for a Democratic presidential candidate, Mr. Biden, for the first time since Lyndon B. Johnson. Representative Elaine Luria, a Democrat and former Navy commander whose congressional district includes Virginia Beach, is among Republicans’ top targets for 2022.The city stretches from saltwater taffy shops on the touristy Atlantic beaches to quiet streets of brick homes that lace around the area’s many bays. Outdoor conversations are interrupted by earsplitting military jets, which rarely draw a glance skyward.Ellen Robinson, a retired nurse, who identifies as a political independent, was “horrified” by the Texas law and said that if the court overturned Roe, “I think it would be the beginning of fascism in this country.”Kathleen Moran, a technical editor in the engineering field, who favors Democrats, said the Supreme Court’s decision on the Texas law “scared” her.“I have boys who will be dating women,” she said. “I have nieces. This goes back to the whole ‘white men get to make all the decisions about everything.’”Ms. Moran said she was more intent on voting after the court declined to halt the Texas law, which the Biden administration is trying to block.“We are in a really dangerous situation,” she said. “Obviously for abortion, we don’t want to become Texas, but on a lot of issues we could lose what is now a blue state.”While many Republican women across Virginia would most likely support stricter abortion laws, few conservative-leaning women in suburban Virginia Beach expressed support for a six-week abortion law or a reversal of Roe v. Wade. Overall, while these women didn’t always embrace the “pro-choice” label, they agreed that women should be able to make their own reproductive decisions.Glenn Youngkin, the Republican candidate for governor in Virginia, dodged a question at a debate about whether he would sign a six-week abortion ban with exceptions for rape and incest.Carlos Bernate for The New York Times“I know Republicans have been against abortion forever, but as a woman, I think I ought to be able to choose myself,” said Janis Cohen, 73, a retired government employee. Her lawn featured a parade of signs for G.O.P. candidates. When it was pointed out that one of them, Winsome Sears, who is running for lieutenant governor, has said she would support a six-week abortion ban, Ms. Cohen fired back that the current governor, the Democrat Ralph Northam, was what she considered an abortion extremist.In 2019 the governor, a pediatric neurologist, seemed to suggest that a delivered baby could be left to die if the mother requested an abortion while in labor with a deformed fetus unlikely to survive. Republicans across the country seized on the comments as sanctioning “infanticide.” Mr. Northam’s office called the accusations a bad-faith distortion of his views.Polls of the Virginia governor’s race have generally forecast a close race, including one by Emerson College last week with the candidates within the margin of error.Nancy Guy, a Democratic state delegate who flipped a Republican-held seat in Virginia Beach by just 27 votes in 2019, said that before abortion rose as an issue in recent weeks, “most people were complacent and not paying attention.”Ms. Guy’s opponent has pledged that if elected, he will donate his salary to a so-called crisis pregnancy center that steers pregnant women away from abortions. The contrast could not be more clear to voters who follow the issues. Still, Ms. Guy said, with the news constantly churning, it is difficult to know what will drive voters nearly two months from now to cast ballots.Nancy Guy, a Democratic state delegate, said that before abortion rose as an issue in recent weeks, “most people were complacent and not paying attention.”Carlos Bernate for The New York TimesDemocrats in Virginia made huge strides during Mr. Trump’s divisive leadership, culminating in 2019, when the party took control of both the State Senate and House of Delegates. But Democrats’ majorities are slim, and Republicans believe they have an anti-incumbent wind at their backs this year. Three statewide positions are on the ballot on Nov. 2 — governor, lieutenant governor and attorney general — along with all 100 seats in the House.The field director for Planned Parenthood Advocates of Virginia said that on average, 10 to 15 volunteers were on door-knocking shifts, compared with 25 to 40 two years ago, a worrying sign for supporters of abortion rights.Han Jones, Planned Parenthood’s political director in Virginia, added: “People are exhausted with elections and exhausted with Donald Trump’s rhetoric and feel like they can take a break. We could easily go red in this election alone if Democratic voters who are not feeling as passionate or leaned in don’t turn out to vote.”A team of Planned Parenthood canvassers who visited a neighborhood of attached town homes recently encountered general support for Democrats, but not much awareness of the election or enthusiasm for it.One voter, Carly White, said abortion was a touchy subject in her household. “I’m for Planned Parenthood but my husband is not,” she said, stepping outside a home with a small, precisely trimmed lawn. “I think the issue is, he’s a man. He’s never grown a baby. I just can’t — I don’t like somebody telling me what I can do with my own body.” More