PROVIDENCE, R.I. — Allan Fung, a former mayor who would be the first Republican in more than 20 years to represent this city in Congress, could hardly make it five feet without being stopped by a supporter on a recent Thursday evening as he tried to maneuver his way from the lobby of a Crowne Plaza to a tent where local business owners had gathered to meet him.In nearby Connecticut, George Logan, a Republican former state senator, switched effortlessly between Spanish and English as he went door to door telling voters in suburban New Britain that he wanted to lower their taxes.“I want to work with Democrats and Republicans,” Mr. Logan, a former state senator, said in an interview between door knocks. “There is no one congressman or woman that I agree with on every topic, 100 percent of the time.”Farther north in Maine, former Representative Bruce Poliquin says in his ads that he wants to bring “Maine common sense” back to Congress, working to distance himself from the far-right tilt of his party as he campaigns to reclaim the seat he lost to Representative Jared Golden four years ago.In an aggressive push in the homestretch of the midterm congressional campaign, Republicans have stepped up their efforts to lay claim to seats in New England, a region that once boasted a proud tradition of electing independent-minded Republicans, but that has more recently slid out of reach of a party that has lurched to the right.They have done so by promoting candidates who are billing themselves as centrists with broad appeal — a far different brand from the hard-right figures and election deniers who make up the critical mass of the G.O.P. — hoping to bolster their chances of winning a substantial House majority in a cycle that has favored Republicans.In Rhode Island, Allan Fung, the former mayor of Cranston and a two-time candidate for governor, is campaigning for Congress on fighting inflation and increasing public safety.Philip Keith for The New York TimesThe turf has hardly been friendly to the G.O.P. in recent years. Republican representation in New England was nearly wiped out in 2006, when only one of the region’s 22 House races was won by a Republican. By 2018, the party was shut out entirely after Mr. Poliquin lost his re-election campaign to Mr. Golden. That left Senator Susan Collins of Maine as the sole remaining congressional Republican in New England.Now, Republican leaders are working to revive the party’s standing with an estranged but critical swath of voters in the region who prefer politicians who do not operate in lock step with the national parties.And Democrats, who have watched with alarm as the Republicans have gained traction, are scrambling to persuade voters that however mainstream these New Englanders may seem, electing them would empower an extremist G.O.P.The State of the 2022 Midterm ElectionsElection Day is Tuesday, Nov. 8.A Pivotal Test in Pennsylvania: A battle for blue-collar white voters is raging in President Biden’s birthplace, where Democrats have the furthest to fall and the most to gain.Governor’s Races: Democrats and Republicans are heading into the final stretch of more than a dozen competitive contests for governor. Some battleground races could also determine who controls the Senate.Biden’s Agenda at Risk: If Republicans capture one or both chambers of Congress, the president’s opportunities on several issues will shrink. Here are some major areas where the two sides would clash.Ohio Senate Race: Polls show Representative Tim Ryan competing within the margin of error against his G.O.P. opponent, J.D. Vance. Mr. Ryan said the race would be “the upset of the night,” but there is still a cold reality tilting against Democrats.In an interview, Seth Magaziner, a Democrat and former teacher and state treasurer who is running against Mr. Fung for an open seat in southern and central Rhode Island, cited his opponent’s support for former President Donald J. Trump and his opposition to a state marriage equality law as evidence that Mr. Fung is no centrist.“The Republicans are trying to package someone who is not a moderate as a moderate,” said Mr. Magaziner, who has trailed Mr. Fung in recent polls. “That has never been his record.”Top Republicans are spending freely to try to strengthen the New England Republicans’ chances.Seth Magaziner, a Democrat, is a former teacher and state treasurer who is running against Mr. Fung.Philip Keith for The New York TimesMr. Magaziner has trailed Mr. Fung in recent polls.Philip Keith for The New York TimesLast week, the Congressional Leadership Fund, a super PAC aligned with Representative Kevin McCarthy, the California Republican and minority leader, poured an additional $1 million into Mr. Fung’s race, tripling its investment. Calvin Moore, a spokesman for the group, said the PAC had spent $3.5 million for Mr. Logan and $5.5 million for Mr. Poliquin.Mr. McCarthy visited Rhode Island in August to raise money for Mr. Fung, and Representative Steve Scalise of Louisiana, the minority whip, attended a fund-raiser for Mr. Fung last week..css-1v2n82w{max-width:600px;width:calc(100% – 40px);margin-top:20px;margin-bottom:25px;height:auto;margin-left:auto;margin-right:auto;font-family:nyt-franklin;color:var(–color-content-secondary,#363636);}@media only screen and (max-width:480px){.css-1v2n82w{margin-left:20px;margin-right:20px;}}@media only screen and (min-width:1024px){.css-1v2n82w{width:600px;}}.css-161d8zr{width:40px;margin-bottom:18px;text-align:left;margin-left:0;color:var(–color-content-primary,#121212);border:1px solid var(–color-content-primary,#121212);}@media only screen and (max-width:480px){.css-161d8zr{width:30px;margin-bottom:15px;}}.css-tjtq43{line-height:25px;}@media only screen and (max-width:480px){.css-tjtq43{line-height:24px;}}.css-x1k33h{font-family:nyt-cheltenham;font-size:19px;font-weight:700;line-height:25px;}.css-1hvpcve{font-size:17px;font-weight:300;line-height:25px;}.css-1hvpcve em{font-style:italic;}.css-1hvpcve strong{font-weight:bold;}.css-1hvpcve a{font-weight:500;color:var(–color-content-secondary,#363636);}.css-1c013uz{margin-top:18px;margin-bottom:22px;}@media only screen and (max-width:480px){.css-1c013uz{font-size:14px;margin-top:15px;margin-bottom:20px;}}.css-1c013uz a{color:var(–color-signal-editorial,#326891);-webkit-text-decoration:underline;text-decoration:underline;font-weight:500;font-size:16px;}@media only screen and (max-width:480px){.css-1c013uz a{font-size:13px;}}.css-1c013uz a:hover{-webkit-text-decoration:none;text-decoration:none;}How Times reporters cover politics. We rely on our journalists to be independent observers. So while Times staff members may vote, they are not allowed to endorse or campaign for candidates or political causes. This includes participating in marches or rallies in support of a movement or giving money to, or raising money for, any political candidate or election cause.Learn more about our process.Representative Elise Stefanik of New York, the third-ranking Republican who denies that the 2020 election was fair, also appeared with Mr. Logan this month at a fund-raising event.One reason the region appeals to Republicans as they look to expand their footprint into even the bluest of states is the makeup of the electorate: Between a third and half of registered voters in New England do not have a party affiliation. They have long been known for rewarding politicians who reach across the political aisle, like Ms. Collins and Senator Angus King, a Maine independent, both of whom have been involved in bipartisan negotiations and supported Democratic-led bills.Republicans are hoping that disaffected Democrats and independent voters will turn to “Republican candidates who are running local races and delivering a more pragmatic message” as a check on Democratic dominance in their states, said Samantha Bullock, a spokeswoman for the National Republican Congressional Committee.At a recent debate, Mr. Logan, who is challenging Representative Jahana Hayes, a second-term Democrat, described himself as a “Connecticut Republican”: moderate on social issues, fiscally conservative. He admonished the Biden administration for its economic policies, blaming Democrats’ large spending bills for rising inflation. But he appeared to share Ms. Hayes’s views on some issues, saying he supported infrastructure investments and abortion rights.Mr. Logan appeared to share the views of Representative Jahana Hayes, the Democratic incumbent, on some issues, saying he supported infrastructure investments and abortion rights.Hilary Swift for The New York TimesMr. Logan later clarified to reporters that he did not think Congress had the constitutional power to codify Roe v. Wade, as Democrats sought to do after the Supreme Court decision this year overturning it.In Rhode Island, Mr. Fung, the first Chinese American to be elected mayor of Cranston and a two-time candidate for governor, is campaigning on fighting inflation and increasing public safety. Mr. Fung said in an interview that he would have supported the $1 trillion bipartisan infrastructure law that President Biden signed last year, as well as an industrial policy measure enacted over the summer, and that he would back legislation to protect abortion access.He denied that he had shifted his positions to appear more moderate, saying that Democrats were “running a lot of this national cookie-cutter playbook, and I just don’t fit their mold.”Mr. Poliquin may be the least centrist of the three, having aligned himself more closely with Mr. Trump and embraced conservative positions on social issues, such as opposition to gun control measures.National Democrats have invested huge sums to counter the G.O.P.’s inroads into New England, working to portray Mr. Fung and the other Republican candidates as far outside the mainstream. The Democratic Congressional Campaign Committee and allied political action committees have spent more than $2.3 million in the Rhode Island race, $3.6 million in Ms. Hayes’s district and nearly $10 million in Mr. Golden’s, according to a spokesman for the Democratic committee.Democratic ads show a smiling Mr. Fung wearing a Trump beanie. Ads against Mr. Poliquin emphasize his support for abortion bans, including his previous backing for legislation that would prohibit abortions after 20 weeks of pregnancy.And in Waterbury, Conn., the campaign staff for Ms. Hayes held signs at a rally before a televised debate that read “Logan [hearts] Trump.” After the debate, Ms. Hayes told reporters that a moderate would not have invited House leaders to campaign in the district or appeared on Tucker Carlson’s Fox News program to share his message, as Mr. Logan did this month.Ms. Hayes tried to paint Mr. Logan as a conservative, referring to his ties to congressional leadership and an appearance on Tucker Carlson’s show on Fox News.Hilary Swift for The New York TimesMr. Logan’s campaign headquarters. Republicans are hoping that disaffected Democrats and independent voters will turn to moderate Republicans.Hilary Swift for The New York Times“He has inextricably connected himself to national Republican leadership,” she said. “They are propping up his campaign with millions of dollars.”Not all voters are swayed by the connection.Dr. Earl Bueno, an anesthesiologist and independent voter from Connecticut, said he supported Mr. Logan, likening the Republican candidate to one of the state’s Democratic senators.“I don’t see him as an extremist that people are painting him as right now,” Dr. Bueno said. “I’m pro-George Logan because, like Senator Chris Murphy, you can actually reach out and have a conversation with him.”Some Democrats are resorting in the final weeks of the campaign to reminding voters that electing any Republican — even a moderate one — could hand the G.O.P. control of Congress.Senator Sheldon Whitehouse, Democrat of Rhode Island, made that point at a recent dinner for Mr. Magaziner at a golf course in Providence.“Please,” he told a group of voters at the dinner, “don’t make Allan Fung the vote that makes Kevin McCarthy speaker of the House of Representatives.” More