SCOTCH PLAINS, N.J. — When New Jersey’s congressional map was redrawn last year, Representative Tom Malinowski, a second-term Democrat, was widely considered a political goner.President Biden’s popularity had plummeted, gas prices were soaring and Mr. Malinowski’s Seventh Congressional District — in which he barely eked out a re-election victory in 2020 — had been redrawn to include nearly 27,000 more registered Republicans. When Mr. Malinowski announced he would run for a third term, he did so in a terse statement, quoting an ominous Shakespearean battle cry: “Once more unto the breach, dear friends, once more.”But 10 months later, as voters have absorbed the impact of the Supreme Court decision overturning the constitutional right to abortion, there are signs that Democrats believe the national political momentum has shifted to a degree that even this race, written off by some as a strategic sacrifice, is narrowing.Any path by which Democrats are able to stave off a midterm rout or retain a slim House majority cuts straight through districts like Mr. Malinowski’s, where moderate, well-educated voters helped Democrats win control of the House in 2018 and are seen as crucial to holding it.“I do see it as a bit of a bellwether — an indicator of how things are going to go nationally,” said Mike DuHaime, a Republican strategist who was a key architect of former Gov. Chris Christie’s victories in 2009 and 2013.Mr. Malinowski is running for a second time against Tom Kean Jr., the namesake of a beloved former New Jersey governor making his fourth run for Congress. Mr. Kean came within about 5,000 votes of winning in 2020 and remains a formidable opponent this year.Still, a national political action committee dedicated to preserving the Democratic majority in the House has suddenly begun buying up its first television time for Malinowski ads. And Democratic loyalists who have been knocking on doors for Mr. Malinowski say concern over abortion rights has grown palpable within the suburban swing district, which stretches from one side of northern New Jersey to the other.“I don’t know a woman who isn’t really angry and really scared,” Jennifer Robinson of Tewksbury, N.J., who supports Mr. Malinowski, said on Sunday night after a forum with both candidates sponsored by the Jewish Federation of Greater MetroWest New Jersey.“Republicans targeted this race thinking Tom Kean Jr. was going to ride a red wave,” said James Singer, a spokesman for the Democratic Congressional Campaign Committee. “Instead, with five weeks to go, this race remains neck and neck.”None of the major independent polling operations in New Jersey have released surveys about the race. A poll conducted in late July, paid for by a group that supports term limits, showed Mr. Kean leading by eight percentage points; 11 percent of the 400 people surveyed said they were undecided.The State of the 2022 Midterm ElectionsWith the primaries over, both parties are shifting their focus to the general election on Nov. 8.Standing by Herschel Walker: After a report that the G.O.P. Senate candidate in Georgia paid for a girlfriend’s abortion in 2009, Republicans rallied behind him, fearing that a break with the former football star could hurt the party’s chances to take the Senate.Democrats’ Closing Argument: Buoyed by polls that show the end of Roe v. Wade has moved independent voters their way, vulnerable House Democrats have reoriented their campaigns around abortion rights in the final weeks before the election.G.O.P. Senate Gains: After signs emerged that Republicans were making gains in the race for the Senate, the polling shift is now clear, writes Nate Cohn, The Times’s chief political analyst.Trouble for Nevada Democrats: The state has long been vital to the party’s hold on the West. Now, Democrats are facing potential losses up and down the ballot.On Sunday, an internal poll memo released by Mr. Malinowski’s campaign suggested that the race had narrowed, and that he and Mr. Kean were statistically tied, 48 percent to 48 percent.Mr. Kean’s campaign spokesman dismissed the poll and called its release a “desperate cry for help.”Mr. Malinowski and three other New Jersey Democrats rode a wave of anti-Trump fervor to Congress during the 2018 midterm cycle, temporarily leaving the state with just one Republican in its 12-person congressional delegation. But many of these newly blue swing districts remained highly competitive.Last year, the new congressional map, redrawn to reflect the 2020 census, eased some of the pressure on Democrats. As it added Republican-leaning towns to Mr. Malinowski’s district, it shored up the districts of several other vulnerable incumbents at a time when Democrats were bracing for a midterm shellacking.The districts of Democratic Representatives Josh Gottheimer, Andy Kim and Mikie Sherrill all shed Republican-leaning towns — territory that in southern and central New Jersey the state’s two Republican congressmen, Christopher Smith and Jeff Van Drew, mainly absorbed, making their seats safer, too. Only Mr. Malinowski’s race, on paper, got harder.Yet until last month, the Democrats’ House Majority PAC had not made ad buys for Mr. Malinowski’s race, even as Republican special interest groups prepared to pump millions of dollars into Mr. Kean’s.But in late September the political action committee began booking television airtime, and it has now reserved between $100,000 and $185,000 in ads each week until Election Day, according to data maintained by Ad Impact, a company that tracks political advertising.Tom Kean Jr. speaking to voters in Scotch Plains, N.J., on Sunday. He came close to winning in 2020.Bryan Anselm for The New York TimesMr. Malinowski’s district includes affluent commuter towns close to New York City, communities filled with horse-country estates (and a former president’s golf course) and rural, Republican bastions. Voters in the district backed Mr. Biden by less than four percentage points, even though he beat former President Donald J. Trump by nearly 16 percentage points in New Jersey, where Democrats outnumber Republicans by just over one million voters.Even if it has narrowed, the race remains a decidedly uphill battle for Mr. Malinowski.Inflation has been stubborn, and consumers are still feeling an economic pinch — an issue that a Monmouth University poll released on Monday found is likely to overshadow abortion access as a motivator heading into the midterms. Only 42 percent of voters across the country support Mr. Biden, according to last month’s New York Times/Siena College poll, a threshold that is just as bad or worse than any president whose party went on to lose control of Congress in midterm elections, going back to 1978.And Mr. Malinowski remains under investigation by the House Ethics Committee over allegations he failed to properly disclose hundreds of thousands of dollars in stock trades, an error he has taken responsibility for and said resulted from carelessness.“It’s better for Democrats than six months ago,” Mr. DuHaime said. “But it’s still a better political environment for Republicans than it was two years ago — and certainly four years ago.”At the forum on Sunday, questions from an audience filled almost entirely with Malinowski supporters centered largely on Mr. Kean’s position on abortion.Mr. Malinowski supports access to abortion at any point in a pregnancy, and he said on Sunday that he would vote to enshrine a right to abortion into federal law.Mr. Kean, a former state senator and assemblyman, has said he supported a “woman’s right to choose.” But he opposes abortion after 20 weeks of pregnancy absent extenuating circumstances, according to his campaign.“I think there are meaningful exceptions that should be rape, incest, life and the health of the mother,” he said Sunday. “Those are exceptions for a reasonable amount of time.”In the Senate, he voted against a bill affirming abortion as a right in New Jersey. He said he opposed the legislation, which was later signed into law, because it permitted abortion at any point in a pregnancy, including what he called late-term abortion. Abortions after 21 weeks of pregnancy are rare, accounting for less than 1 percent of all abortions performed in the United States in 2019, according to the Centers for Disease Control and Prevention.A Kean campaign website is less nuanced.“Tom is a fierce defender of the sanctity of life, fighting every step of the way to protect the unborn from egregious abortion laws proposed in New Jersey, and will continue to do so in Congress,” it reads.“When I’m talking about the egregious piece of legislation, the ability to choose to terminate, for not valid reasons, when a baby can stay alive, be alive, outside of the womb, is wrong,” he said at the forum.Of the 616,000 registered voters in the district, about a third are not enrolled in either major party. It is these moderate voters who tend to sway elections in New Jersey.Motivating supporters to turn in mail ballots or to show up at polling places during an election year with no statewide races is crucial for any candidate, said Debbie Walsh, director of the Center for American Women and Politics at Rutgers.“Elections are about turnout,” Ms. Walsh said. “The people who turn out are the people who feel they have the most at stake.”Ms. Walsh, whose organization studies voting trends among women, said she believed the Supreme Court decision that overturned Roe v. Wade and ended nearly 50 years of abortion rights in the United States would be an “energizer.”“I think it all feels very real to people,” she said.Tracy Keegan, a founder of Summit Marches On, a left-leaning group in Mr. Malinowski’s district that formed after the 2017 Women’s March and includes mainly women with children, said she believed the growing energy among voters extended beyond concern over reproductive rights.“It’s not just about abortion,” she said. “It’s about a government’s willingness to remove freedoms.”A gun control rally in Summit, N.J., after the mass school shooting in Uvalde, Texas, drew hundreds of people, said Ms. Keegan. a 51-year-old mother of three.“It wasn’t just Democrats,” she said. More