Glenn Youngkin was waving off talk about running for the White House back in 2021, before he’d even made it to the Virginia governor’s mansion.

Brad Hobbs, a childhood friend, told The Associated Press at the time that his ultimate goal was to see the Harvard-educated Republican businessman run for president. Mr. Hobbs said he brought it up nonstop, even in front of others, which irked Mr. Youngkin.

“He doesn’t commit to that. He looks at me like, ‘Stop saying it; I don’t want to hear that,’” Mr. Hobbs said.

Conjecture that Gov. Youngkin, who is set to host a major donor retreat Tuesday and Wednesday, might make a late entry into the 2024 presidential race has only grown since his victory nearly two years ago. It could further escalate after next month’s high-stakes legislative elections, where he’s aiming for a GOP sweep.

At least some of the recent talk is coming from Republican donors still casting about for yet another alternative to former President Trump.

But the 56-year-old Gov. Youngkin, who in public remarks has demurred but not totally shut the door to a bid, would face logistical campaign difficulties, ballot access hurdles and — according to interviews around the country over the past week — skepticism from some Republican voters, who either don’t know him well or are locked in on Mr. Trump.

“I think it’s ill-conceived and a really horrible idea,” Eric Levine, a New York-based attorney and Republican donor who has urged his party to back someone other than Mr. Trump, said of a potential Youngkin candidacy. “It is doomed to failure and will only damage his brand.”

Gov. Youngkin, who answers questions about his presidential prospects by saying he’s flattered to be in the conversation but focused on Virginia, is currently in the midst of the hectic final push to the state’s Nov. 7 election, with early voting already underway.

Every seat in the General Assembly is on the ballot, and both parties see a possible path to a legislative majority in a state that once seemed destined to move from red to blue but now hangs in the balance. If Republicans manage to hold the House of Delegates and flip the Senate, that would give Gov. Youngkin broad leeway to enact more of what he calls his common sense conservative priorities — including additional tax cuts, new limits on abortion and a rollback of clean energy mandates — over the final two years of his time in the governor’s mansion. Virginia uniquely prohibits its chief executives from serving consecutive terms.

Gov. Youngkin, known for his folksy, high-energy style, launched a major early voting push this cycle, shattered previous governors’ fundraising records, campaigned with candidates and is in the weeds on the specifics of battleground races, according to his advisers.

On Tuesday and Wednesday, Gov. Youngkin and his wife, Suzanne Youngkin, will host a second annual “Red Vest Retreat,” a nod to the governor’s signature campaign attire, at an elegant hotel in Virginia Beach, according to an invitation obtained by the AP. Details of the retreat were first reported in The Washington Post.

“Obviously there are a lot of folks that are encouraging him ... who like what he has done in Virginia, what he’s been able to accomplish, and would love to have him do that on the national level. But again, his focus is going to continue to be on Virginia and these elections,” said Dave Rexrode, a senior adviser to Gov. Youngkin, in an interview.

The retreat is for individuals who are financial supporters of the governor’s Spirit of Virginia PAC, said Mr. Rexrode, who is chairman of the organization. No presidential candidates were invited, and Mr. Rexrode declined to share details of the agenda ahead of the event.

The speculation around a Youngkin run has been driven not only by his upstart win but also his travel around the country, frequent conservative media appearances, highly-produced public events, record-breaking fundraising and his refusal to shut down the prospect.

Should he decide to make the leap after next month’s elections, a potential campaign would face significant logistical hurdles.

With less than 100 days until voting starts with Iowa’s leadoff caucuses, Gov. Youngkin does not have the kind of campaign organization that a presidential hopeful needs to recruit supporters for caucuses or get voters to turn out in January. Most of the presidential campaigns have been organizing since early 2023. Mr. Trump also has enormous name recognition, years of organizing experience and established supporters nationwide.

Before Gov. Youngkin could even worry about turning out supporters, he’d be up against crucial deadlines.

While there’s no deadline to become a candidate for Iowa’s caucuses, competing there takes months of securing supporters who will agree to show up at a certain time and place. The deadline to file for the second contest, New Hampshire’s primary, is Oct. 27. Other states’ deadlines start rolling in soon after, with Alabama and Arkansas requiring candidates to collect signatures from voters and file their candidacy days after this November’s election.