By design or accident, O’Rourke’s extended period of indecision has generated a suspense around his decision that few other candidates can match. He intensified interest this week by telling reporters that he and his wife had made a decision and were “excited to share it with everyone soon.”

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Aides have been discussing how to handle, for example, campaigning in Iowa. And those around O’Rourke have been receiving unsolicited résumés, offers to have O’Rourke stay at private homes, and — from one supporter — an offer to donate the website domain betosback.com.

Some have asked whether they can start donating to his campaign (they cannot), or inquired into why their recurring payments to his Senate campaign have stopped (the committee was shut down).

In remarks to reporters last week in El Paso, O’Rourke set himself apart from other prominent Democrats who call themselves socialists.

“I’m a capitalist,” O’Rourke said. “I don’t see how we’re able to meet any of the fundamental challenges that we have as a country without in part harnessing the power of the market. Climate change is the most immediate example of that. If you’re going to bring the total innovation and ingenuity of this country to bear, our system as a country, our economy, is going to have to be part of that.”

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A nucleus of advisers in El Paso, O’Rourke’s hometown, has been holding strategy meetings — and going on hikes with O’Rourke — as they plan for a nascent campaign. The former congressman has been riding his bicycle to a makeshift office near San Jacinto Plaza, making calls and soliciting advice from Democrats around the country.

Some supporters have advised him to run a campaign in Iowa similar to the Texas effort that made him a national figure, when he drove around in a Chevrolet Suburban, visiting communities Democrats typically bypassed and live-streaming almost everything on Facebook.

“He brings a fresh personality that is perhaps distinctive and creates his own niche in a way comparable to what Obama did,” said Kurt Meyer, chairman of the Tri-County Democrats of Iowa.

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Meyer has met with Democratic Sens. Elizabeth Warren of Massachusetts and Sherrod Brown of Ohio, and Sen. Cory Booker (D-N.J.) has stayed at Meyer’s home. Warren and Booker are running for president, and Brown is weighing a run.

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“Some of this would be more personality- and aura-driven than necessarily position-driven,” Meyer said. “I think at least the personality and aura of Beto O’Rourke would mean that Iowans would have to take a look.”

An O’Rourke candidacy could add a centrist, upbeat message to a campaign that has been marked by left-leaning policies and sometimes anger, and it could sharpen the question for Democratic voters of which direction they want to go in the age of President Trump.

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If O’Rourke jumps in, a move that could come as early as next week, it would answer one of the biggest uncertainties hovering over a turbulent early primary season, leaving former vice president Joe Biden as the most prominent remaining undecided figure.

The Texan could be an un­or­tho­dox candidate: He resists labels, is wary of the party establishment and has operated without a pollster or a speechwriter. His appeal rests largely on personality rather than policy; he projects a youthful, hipster quality at age 46 but is largely untested on the national stage and would have one of the lightest résumés in a crowded field of senators, governors and perhaps a former vice president.

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“There’s no question that he has that intangible quality where people want to follow him and raise money for him and volunteer for him,” said Jen Psaki, a longtime Democratic consultant who has worked on several presidential campaigns.

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“The questions that are unknown is: Can he scale up the sort of magic that he created in Texas? We don’t know that,” she said. “And the second question is: What unique ideas does he bring to the table on the policies that people care about?”

O’Rourke is not the only Democrat with a notable following — Sen. Kamala D. Harris (D-Calif.) has attracted sizable crowds, and Sen. Bernie Sanders (I-Vt.) has shown impressive fundraising. Some liberals are wary of O’Rourke’s ideological vagueness at what they consider a rare moment for left-leaning ideas.

Beyond that, political history is full of candidates who were initially seen as powerhouses, only to have their campaigns sputter once they faced a presidential race with its unique pressure and exposure.

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It is not clear how O’Rourke would fit into a field that so far has been largely shaped by outspokenly liberal candidates. A fourth-generation Irish-American who speaks fluent Spanish, O’Rourke was part of the centrist New Democrat Coalition during his time in Congress.

Asked recently if he was a progressive, he demurred. “As you may have seen and heard over the course of the campaign, I’m not big on labels,” he told reporters. “I don’t get all fired up about party or classifying or defining people based on a label or a group.”

O’Rourke was largely unknown until his campaign last year against Sen. Ted Cruz (R-Tex.). He appeared on “The Ellen DeGeneres Show” and had backing from celebrities including Beyoncé, LeBron James and Broadway star Lin-Manuel Miranda. He raised record amounts of money and skillfully harnessed social media.

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His three-point loss to Cruz, in a highly conservative state, did little to diminish the excitement among some Democrats for him to launch a presidential campaign.

He has met with former president Barack Obama, and was encouraged by many in Obama’s network to consider a run. He also went on a solo journey, which he documented in posts on the website Medium that revealed he had found himself “in and out of a funk.”

O’Rourke is scheduled to appear March 9 at the premiere of a documentary on his Senate campaign, to be screened at the South by Southwest festival in Austin. A group of other 2020 candidates — including Warren; Sen. Amy Klobuchar (D-Minn.); Pete Buttigieg, the mayor of South Bend, Ind.; and former San Antonio mayor Julián Castro — are also appearing at the festival.

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The Dallas Morning News reported on Wednesday that O’Rourke has decided not to run for U.S. Senate in 2020. Senate Minority Leader Charles E. Schumer (D-N.Y.) in recent weeks has been encouraging O’Rourke to run against Sen. John Cornyn (R-Tex).

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Meanwhile, a group of reporters from national news organizations has been camping out in El Paso, awaiting any announcement. CNN cameras on Thursday filmed O’Rourke unlocking his bicycle from a street sign.

“You didn’t get my code, did you?” he asked, joking that someone might steal his bike.

Then, as he began to pedal off, he answered one last question.

“Fixie?” someone asked, referring to a type of simple bicycle. “It was,” he said. “I just put a freewheel on it.”