“We could have picked apart this guy,” one Republican leader in New Mexico said of Solomon Peña, who is accused of organizing attacks on the homes of four Democratic officials.ALBUQUERQUE — The former Republican candidate accused of targeting the homes of Democrats in drive-by shootings had routinely called for locking up 2020 election officials in Guantánamo Bay. He promoted conspiracy theories about solar power, feminism and “the demonic theories of the Globalist Elites.” He had been demoted twice by the U.S. Navy and served nearly seven years in prison for burglary.Yet powerful party leaders in New Mexico not only gave the first-time candidate, Solomon Peña, 39, full-throated endorsements, they also opened their checkbooks to fund his race for a state legislative seat in central Albuquerque long held by Democrats. Some knew about his prison record but said they felt that he had turned his life around. Local and state authorities now say they are investigating whether drug money helped fund his campaign.“He came across to me as a very respectful, thoughtful young man,” said Harvey Yates, an oilman and former chairman of the New Mexico Republican Party, who donated $5,000 to Mr. Peña’s election effort. Now, Mr. Yates acknowledges that he may have made a mistake. He said that he felt “very bad, very sad” for Mr. Peña, “who I think really had possibilities.”The police say that after losing his race by a landslide in November — he received 26 percent of the vote — and refusing to concede, Mr. Peña organized shootings at the homes of prominent Democrats, including two who certified the election results. The attacks came at a time of growing fears across the country about a trend of political violence, mostly from the right wing, including the attack on the husband of then-Speaker Nancy Pelosi, a conspiracy to kidnap Gov. Gretchen Whitmer of Michigan and the mob attack on the U.S. Capitol on Jan. 6, 2021.In New Mexico, the case also highlights the internal struggles among Republicans as election deniers like Mr. Peña — who was in the crowd for President Donald J. Trump’s speech in Washington on Jan. 6, according to videos collected by online sleuths — fill the ranks of candidates seeking elected office. Other Republicans such as Audrey Trujillo, who ran for secretary of state, embraced conspiracy theories about elections, school shootings and Covid-19 vaccines.Many of those election deniers lost in New Mexico, mirroring similar Republican setbacks in other parts of the country. The results helped the state’s Democrats solidify their control of both houses in the state Legislature, the governor’s office and the entire congressional delegation, sparking recriminations over the Republicans’ loss of power.Michael Candelaria, a prominent state Republican who until recently was the party chairman in Valencia County, near Albuquerque, said the Peña case laid bare a dilemma in a state where Democrats have steadily expanded their sway in recent years: how to appeal to some of Mr. Trump’s most ardent supporters, who refused to accept his 2020 re-election defeat, without alienating other voters who reject the lies and conspiracy theories.“You don’t take a group of people whose support you want and tell them, ‘You’re a bunch of crazies,’” Mr. Candelaria said. “You’re going to have some extremists that you have to figure out how to keep their support.”But Mr. Candelaria, who has pushed for leadership changes in the state party, said that Mr. Peña’s arrest showed the risks of promoting such figures. “Had we done some good vetting, we could have picked apart this guy, but no, we don’t do a good job of picking candidates,” he said.It was unclear how much Republican leaders had examined Mr. Peña’s background. Steve Pearce, a former member of Congress who is now chairman of the New Mexico Republican Party, did not respond to requests for comment.Some Republicans are now bracing for more revelations about Mr. Peña, who was arrested on Monday and charged with criminal solicitation, attempted aggravated battery, shooting at an occupied dwelling, shooting from a moving vehicle and conspiracy. The police called him the “mastermind” behind a conspiracy in which four other men were paid to shoot at the homes of two county commissioners and two state legislators, and said that he personally participated in at least one of the shootings.As part of their investigation, Albuquerque police detectives said they were also examining whether Mr. Peña used proceeds from narcotics trafficking to finance his campaign, and whether campaign laws were violated. The New Mexico attorney general’s office will lead the investigation into Mr. Peña’s campaign finances, a spokeswoman for the office said on Friday.The turn in the investigation came after detectives learned through witness interviews that Mr. Peña had identified individuals to funnel contributions from an unknown source into his campaign, according to Gilbert Gallegos, a spokesman for the department. Investigators said they are focusing on José Trujillo, who is also accused in the shootings, and Mr. Trujillo’s mother, Melanie Griego, who are listed as donating a total of $9,150 to Mr. Peña’s campaign.Police arrested Mr. Trujillo on Jan. 3, shortly after the shooting targeting the Albuquerque home of Linda Lopez, a state senator. In the car that Mr. Trujillo was driving, which the police say is owned by Mr. Peña, investigators say they found 893 fentanyl pills and $3,036 in cash, as well as a firearm matching shell casings found at Ms. Lopez’s home.Mr. Peña made his first court appearance on Wednesday and did not enter a plea. Roberta Yurcic, a lawyer representing him, said she couldn’t comment on specific aspects of her client’s background, including his military demotions and work history. “The investigation into the charges against my client is ongoing,” she added. “Mr. Peña has a right to a fair trial.”Javier Martinez, a Democrat whose home was targeted in the attacks after the November election, said that he had “never experienced anything like this before.” Mr. Martinez, who took over this month as New Mexico’s speaker of the House, tied Mr. Peña’s extremism to the election lies voiced by Mr. Trump.“The previous president, I think, really exploited some of those feelings,” Mr. Martinez said. “And we’ve seen it play out in different ways, including the insurrection in Washington, D.C., including this set of events here in our own backyard.”Mr. Peña presented himself as someone on the mend, leading groups in prayer at political meetings and telling neighbors that he did not drink or take drugs. But he made little effort to hide his extreme views. His campaign website denounced “the demonic theories of the Globalist Elites and their foreign counterparts,” called feminism “demonicism,” and said the 2020 election had been rigged against Mr. Trump by “enemy combatants” who “must be placed in Guantánamo Bay, Cuba, for the remainder of their natural lives.”During his campaign, Mr. Peña highlighted his time as a Navy hospital corpsman assigned to a Marine division in Okinawa, Japan. But promotion data provided by the U.S. Navy’s public affairs office shows that Mr. Peña hardly served with distinction. He was demoted twice during his four years in the service and left the military in 2004 at the lowest possible rank. The Navy was unable to provide the reasons for Mr. Peña’s demotions.Mr. Peña ran on a platform of cracking down on crime, despite his own criminal history. He served nearly seven years in prison in New Mexico on charges including burglary and larceny after being part of a “smash-and-grab” crew that slammed vehicles into retail stores, including a Kmart in Albuquerque, then stole items, according to court records.After being released from prison in 2016, Mr. Peña tried selling cars at a dealership in Albuquerque but lasted less than a month before he was fired for showing up late, court records from a lawsuit filed by Mr. Peña in 2017 show. (The case was dismissed.) Mr. Peña also enrolled at the University of New Mexico, obtaining a political science degree in 2021, the same year that his voting rights were restored after his prison term.Mr. Peña appears to have run for the Republican nomination for the state legislative seat unopposed. In October, he received an endorsement from the Republican National Hispanic Assembly’s New Mexico chapter. Ronnie Lucero, the chairman of both the group’s national organization and the state chapter, said that he had spoken with Mr. Peña at events during the campaign, and that the candidate had filled out a questionnaire asking about his professional, financial and criminal history before the group endorsed him.The group did not see Mr. Peña’s criminal record as disqualifying, Mr. Lucero said, adding: “At the time that we made the endorsement, there was the impression that he’d got his life together and he’s one of those second-chance stories that would turn out to be something good and positive for the community.“It was a bad decision that we made, and regretfully,” he said. “But we can’t read the future.”When asked about some of the extremist rhetoric on Mr. Peña’s campaign website, Mr. Lucero said that he had not seen the statements — although they were published before the endorsement, according to the Internet Archive — and that they would have given him pause if he had.Some Republican officials defended the apparent lack of vetting before the party establishment put its support behind Mr. Peña, which included defending him when his opponent sought to have him disqualified from the race because of his criminal record, which could potentially have prohibited him from taking office.“The Republican Party did not recruit him,” said Representative Bill Rehm, a Republican state legislator from Albuquerque, adding that he did not think the party establishment should vet candidates. “He, like anyone else, can sign up to run for whatever office.”John Ismay More