Gov. Bruce Rauner is suffering a major conservative backlash — dissed by a leading magazine of the right this week and bracing for a potential Republican primary challenger next week.

But the first-term governor apparently hasn’t ruffled all the feathers of his party’s right wing.

Billionaire Charles Koch donated $5,600 to Rauner’s campaign fund this week. Koch and his brother David are the nation’s top conservative donors.

The left immediately blasted Rauner for accepting the support.

“This donation proves what many have long suspected: Bruce Rauner is the Koch Brothers’ favorite governor,” said Jake Lewis, campaign director for Illinois Working Together, a coalition of labor organizations.

“Unfortunately for these right-wing billionaires, no amount of Koch money will hide Gov. Rauner’s failure to grow jobs or fix Illinois’ finances.”

Rauner does have some history with the brothers.

He was one of the three Republican governors who attended the annual summit the Koch brothers hosted in California in January.

That trip drew similar harsh criticism from labor, with one union blasting the governor for “huddling” with the Koch brothers as refugees were stranded at airports during the initial implementation of President Donald Trump’s travel ban.

“In one of our darkest hours, he’s plotting with billionaires on how to make the rich richer,” the Illinois Federation of Teachers fumed at the time.

Rauner’s campaign shrugged off the criticism.

“Gov. Rauner is fighting for lower taxes, better schools, and safer communities,” spokesman Justin Giorgio said. “It’s time to work together to accomplish these goals.”

But for Rauner, the relatively small contribution Tuesday — tiny in comparison to the $2.6 million that friend and mega GOP donor Richard Uihlein gave Rauner — could be a signal that the rookie governor still has friends on the right.

His problems with his party’s conservative wing blew up this summer and fall.

The governor outraged conservatives when he signed a bill expanding taxpayer funding of abortion in September, after earlier vowing to veto it. Conservatives Republicans accused him of betrayal, with one former ally of the governor dubbing him “Benedict Rauner.”

That came shortly after Rauner signed a bill to protect undocumented immigrants from deportation, a move that brought criticism from the Trump Administration.

The series of decisions prompted the conservative National Review this week to declare Rauner “the worst Republican governor in America” in a scathing cover story in the December issue.

The article included quotes from state Rep. Jeanne Ives, R-Wheaton, who plans to file petitions on Monday to challenge Rauner in the March primary.

“Republicans understand that Governor Rauner is unelectable,” Ives said in a statement Thursday. “He betrayed his party’s values. He broke promises. And lied about his intentions, most notably on a bill that forces taxpayer funding of abortion on demand.”