Manchin for president? Not as far-fetched as it sounds.

Come on. Sen. Joe Manchin III (D-W.VA.) isn’t going to run for president, even though he told CBS News’s “Face the Nation” on Sunday: “I’m not taking anything off the table, and I’m not putting anything on the table.”

Let’s just think through how a Manchin presidential bid would shake out.

Manchin would be roadkill in a Democratic primary challenge to President Biden; many Democrats can’t stand Manchin. They saw him as an infuriating obstacle in the last Congress, one of their rare stretches of enjoying Democratic control of the White House, Senate and House.

The list of Democratic grievances against Manchin includes: He is prolife-ish (if often contradictory), progun-ish (again, somewhat contradictory) and a thorn in the side of the party’s agenda on climate change. Manchin voted in 2018 to confirm Brett M. Kavanaugh to the Supreme Court, calling him “a qualified jurist who will follow the Constitution and determine cases based on the legal findings before him.”

You could imagine frustrated progressives agreeing to sell their souls in exchange for a big-name challenger to the 80-year-old Biden, and then Satan devilishly serving up the alternate option of 75-year-old Manchin.

Even though so many Democrats abhor him, Manchin also wouldn’t succeed if he switched parties and ran for the GOP nomination. Republicans can’t stand Manchin because last year he agreed to the Inflation Reduction Act and votes with Biden 88 percent of the time. Manchin can talk a good game on the deficit and fiscal restraint, but rarely can find a spending program he doesn’t want to expand, never mind cut.

That leaves running as an independent, which is, of course, the longest of long shots. The scenario could leave the country with a potential bumper crop of geriatric populists: Donald Trump, Manchin and Biden.

The president — widely expected to announce his 2024 bid, likely next month — showcased the populist theme of his reelection bid with the recent State of the Union address. Biden pledged to “offer every American a path to a good career whether they go to college or not,” and declared his “economic plan is about investing in places and people that have been forgotten. . . . Amid the economic upheaval of the past four decades, too many people have been left behind or treated like they’re invisible.” Biden seems determined that no one will outpopulist him in 2024.

One curious complication in the talk about independent bids is the organization No Labels, which plans to field a bipartisan “unity ticket” in 2024, and reportedly has $46 million pledged or raised for this effort. That isn’t much, by presidential campaign standards, but it’s a start. The organization Third Way and other Democrats fear that if the proposed No Labels bipartisan unity ticket becomes reality and gets on the ballot in enough states, it could help elect Trump with a plurality. Manchin is reportedly one of the potential candidates that No Labels is contemplating.

Then again, if any figure would gain traction as an independent, maybe it would be someone such as Manchin, who could run on an authentic message of, “I don’t march in lockstep with anybody — America knows I have annoyed everyone in Washington at one point or another.”

Yes, Manchin’s positions on abortion and guns can turn into a contradictory mess. But Americans themselves have contradictory feelings on abortion, and generally support Second Amendment rights, but then, after mass shootings, tell pollsters they want more gun-control proposals.

Americans also tell pollsters they’re concerned about the debt, but they also don’t want anything to change regarding Social Security, Medicaid or Medicare, and they want to lower taxes and they don’t want any spending cuts that could affect them.

Manchin’s positions might be muddled and inconsistent, but they also reflect Americans’ own muddle and inconsistent preferences.

Manchin became a powerful senator by meeting with everyone, getting along with almost everyone and often brokering half-a-loaf deals that never give one side everything it wants. You can accuse him of always having his finger to the wind, but that means he always knows which way the wind is blowing. Like it or not, that’s a good skill to have when you’re trying to win an election.

No Labels wants a candidate; Manchin loves being the center of attention and between the two parties. What’s more, his bid for Senate reelection in West Virginia next year, when his state is likely to support the Republican presidential candidate, could be challenging.

Hmm. Maybe “Manchin 2024” isn’t quite as unthinkable as it first seemed.