The family of Xana Kernodle is livid over the plea deal offered to accused murderer Bryan Kohberger … and they told prosecutors they had better not dare go through with it.

Kim Kernodle, Xana’s aunt — who was so furious she was in tears — tells TMZ … prosecutors floated the idea of a plea deal a few days ago and the family made it clear … NO WAY.

When we spoke with Kim, she was on a conference call with prosecutors. She says prosecutors told her the defense approached prosecutors with a plea deal, and the prosecution went along to “spare the families” the pain of a trial. Kim says that’s ridiculous, because at least 2 of the families — hers and the Goncalves family — wanted Kohberger to face a jury.

Kim also says when her family got a call from prosecutors a few days ago about a deal, they were vague … prosecutors never mentioned taking the death penalty off the table.

What’s especially puzzling … Kim says prosecutors told her there was enough evidence to secure a guilty verdict.

As we reported, under the deal, Kohberger will plead guilty to 4 counts of murder and in return prosecutors will take the death penalty off the table. Prosecutors will recommend life in prison without the possibility of parole.