CBS News’ marquee morning and evening shows — including the network’s “Late Night with Stephen Colbert” — are heading for record-low ratings this month, The Post has learned.

“CBS Evening News,” hosted by newly-minted anchor Tony Dokoupil, is on pace for its lowest-rated January since at least 2000, according to Nielsen data. The show has averaged 4.3 million viewers, with 560,000 of them in the coveted 25- to 54-year-old demographic

By comparison, the program got a massive ratings spike back in 2006 when Katie Couric debuted as anchor, drawing 14 million viewers just that night.

Dokoupil’s low monthly average comes despite posting a viewership high of 6.4 million viewers on Monday.

“CBS Mornings,” co-hosted by Gayle King and Nate Burleson, is also heading for its lowest-rated month on record, delivering 1.7 million total viewers and 258,000 viewers in the 25-to-54 demographic.

Meanwhile, “CBS Saturday Morning,” which is co-hosted by newly-minted anchors Adriana Diaz and Kelly O’Grady, is on pace for its lowest-rated January ever, averaging 1.6 million total viewers and 207,000 viewers in the key demo.

Even CBS’ “Late Night with Stephen Colbert” is on track to turn in its worst-performing January ever among viewers in the 25- to 54-year-old demo, averaging just 285,000 viewers.

CBS News is in the midst of an overhaul under editor in chief Bari Weiss, who joined the company in October with a mandate to bring a more balanced viewpoint to the network.

“Bari Weiss has her work cut out for her,” a CBS source told The Post, calling the turnaround of the third-place news network a “Herculean task.”

The ratings of CBS’ three main news shows had been plummeting before Weiss arrived, with the source noting that a core problem for the programs — plus Colbert’s show — is that they tend to speak to an audience of coastal elites.

Sources pointed to left-leaning Colbert’s consistent drumbeat of criticism of President Trump, which some critics say has turned off viewers. Colbert’s show has been canceled by CBS, which cited financial reasons for the decision. His last show is in May.

One news exec linked CBS News’ flailing ratings to polarizing coverage that has alienated middle America, pointing to a previous report by The Post on “CBS Mornings” and its provocative bookings.

“When will CBS learn that you have to program for the whole country and not just the coasts?” the source said.

Another CBS insider speculated that the problem isn’t elitism — loyal viewers may be turned off by Weiss’ sweeping changes.

“It’s certainly an indication that America is turning off CBS News. Maybe the appointment of Bari Weiss has alienated CBS viewers?” the person opined.

CBS News did not immediately return requests for comment.

Weiss’ shakeups at the network include replacing “CBS Evening News” co-hosts Maurice DuBois and John Dickerson with Dokoupil, who had co-hosted the flagging “CBS Mornings” alongside King and Burleson.

So far, “Evening News” under Dokoupil, has posted and average of 4.3 million total viewers its first two weeks, but was down 1 million total viewers compared to roughly a year ago.

Although the anchor appears to be getting his footing, he trails “ABC World News Tonight with David Muir” and “NBC Nightly News with Tom Llamas” by big margins. Muir’s show pulled in 8.2 million while Llamas nabbed 6.7 million viewers for the week of January 12.

Meanwhile, Weiss is setting her sights on “CBS Mornings,” approaching star anchor King about taking a special correspondent gig and halving her estimated $13 million salary, The Post reported. Sources also said that Burleson is likely to be moved off the show amid an overhaul of the program — ratings for which are consistently below 2 million.

Weiss and CBS News president Tom Cibrowski have also shakend up “CBS Saturday Morning,” ousting co-anchors Dana Jacobson and Michelle Miller and replacing them with Diaz and O’Grady this month.

Sources with knowledge of the matter cited cost-cutting as a key reason for that change, and said more layoffs are slated in the coming weeks as Weiss looks to overhaul other areas of the network. That includes the staff of “60 Minutes,” as recently reported by The Post.