Mr. Santos, a Republican House member from New York, has admitted to lying about parts of his biography and is facing several ethics and criminal inquiries.Representative George Santos won his seat in Congress in part by deceiving voters with lies and exaggerations about his biography. Now, with his falsehoods exposed, Mr. Santos plans to test his luck with voters again.Mr. Santos, a Republican from New York, formally announced that he was running for re-election on Monday. In a statement, he did not address the controversy that has surrounded him for months.Instead, he depicted himself as a political outsider who would eschew traditional Republican Party politics.“We need a fighter who knows the district and can serve the people fearlessly, and independent of local or national party influence,” Mr. Santos said. “Good isn’t good enough, and I’m not shy about doing what it takes to get the job done.”The announcement follows months of speculation over Mr. Santos’s political future, with fellow Republican lawmakers calling for his resignation, and federal and state prosecutors and his colleagues in Congress investigating his falsehoods on the campaign trail and his finances.Last month, Mr. Santos filed paperwork indicating his intent to run for re-election, but Monday’s announcement, which was first reported in The New York Post, was his first public declaration of his 2024 campaign.Though he has admitted to fabricating some parts of his résumé and biography, Mr. Santos has stood by other apparent falsehoods and insisted that the inquiries into him would find no criminal wrongdoing. Still, for months, he remained publicly ambivalent about whether he would run again.Shortly before sharing his intention to run for re-election on social media, Mr. Santos declined to confirm the announcement, telling a New York Times reporter, “I’m not confirming anything for you.”Mr. Santos enters the race with significant challenges. Polling has shown that he is unpopular in his district, with 78 percent of constituents believing that he ought to resign, according to a January Siena poll.He will also face a cash crunch: As of the end of last month, his campaign had just over $25,000 on hand, according to reports filed with the Federal Election Commission.While other first-term Republicans in New York battleground districts raised hundreds of thousands of dollars in the first three months of the year, Mr. Santos raised only $5,333.26. During that same period he refunded nearly $8,400, bringing his fund-raising total into the negative.That is less than Mr. Santos raised during his first run for office in 2020, when he was virtually unknown and reported receiving about $7,000 in the same three-month period.Around the same time Mr. Santos made his intentions public, Republicans filed paperwork to create a new joint fund-raising committee that will allow Speaker Kevin McCarthy and others to pour money into defending the party’s seats in New York. Mr. Santos was the only vulnerable Republican left out of the effort.Even before he was mired in scandal, Mr. Santos was already expected to face a competitive race.Democrats, eager to reverse losses in New York that cost them their hold on Congress, were eyeing Mr. Santos’s suburban district, which covers northern Nassau County on Long Island and a small section of northeast Queens.But Mr. Santos’s seat became even more of a priority for Democrats after The New York Times and other news outlets published revelations that he had omitted key details from his financial disclosures and misled voters about his education, his professional background, his heritage and his ties to tragedies like the Pulse nightclub shooting and the Sept. 11 attacks.Subsequent reporting uncovered a number of irregularities in his campaign filings, including an unusual pattern of payments for $199.99, an unregistered fund that purported to be raising huge amounts for Mr. Santos and thousands of dollars in unexplained expenses.The F.B.I., federal prosecutors in Brooklyn and the Nassau County district attorney’s office are now all investigating Mr. Santos’s campaign finances and how Mr. Santos operated his business, the Devolder Organization, about which he has disclosed little information.The House Ethics Committee, which is split evenly between Democrats and Republicans, is conducting an inquiry into whether Mr. Santos failed to properly fill out his financial disclosure forms, violated federal conflict of interest laws or engaged in other unlawful activity during his 2022 campaign.Mr. McCarthy, who holds a slim majority in the House, has pinned Mr. Santos’s fate in Congress on that investigation. Yet the speaker, who supported Mr. Santos’s campaign in 2022, has also expressed reservations about a re-election bid, telling reporters in Washington earlier this year that he would “probably have a little difficulty” supporting one.Mr. Santos temporarily removed himself from two congressional committees at the direction of House leadership, and many rank-and-file Republicans have said they would not work with him on legislation.“From a political point of view, I don’t think there’s any future for him,” Edward F. Cox, the state Republican Party chairman in New York, said in an interview. He added that his organization would “clearly not” be helping Mr. Santos’s campaign.Gerard Kassar, the chairman of the New York Conservative Party, a small but influential partner to the Republican Party, said in a statement that the Conservatives would not back Mr. Santos under any circumstances. “The party has called for his resignation and finds his pattern of deceit morally repugnant,” he said.Closer to home, just days after Mr. Santos was sworn in, a score of Republican officials in Nassau County called on him to resign, said they would not endorse him in 2024 and would work to circumvent his office whenever possible.Mr. Santos already faces a primary challenger, Kellen Curry, whose campaign biography says he served in the Air Force for eight years before working for J.P. Morgan.The seat is also being looked at by a raft of Democrats, including Mr. Santos’s 2022 opponent, Robert Zimmerman, and Josh Lafazan, a centrist Nassau County legislator who has entered the race.Party leaders are also encouraging a comeback attempt by Thomas R. Suozzi, the district’s former representative who retired last year. Mr. Suozzi is now working for a consulting firm, but he has spoken about the possibility in recent weeks with Representative Hakeem Jeffries of New York, the top House Democrat, and Jay Jacobs, the state party chairman, according to two people with direct knowledge.Nicholas Fandos More