(CNN) Republican National Committee chairwoman Ronna Romney McDaniel, during a conversation about Arizona GOP Sen. Jeff Flake, said Monday that 2016 Republican senate candidates who did not back President Donald Trump during his presidential run and lost should serve as a "cautionary tale."

Flake, who just released a new book and is up for reelection in 2018, is a prominent critic of Trump.

McDaniel made the comments during a interview on the "Laura Ingraham" show. Ingraham repeatedly questioned if Flake could be kicked off the Republican ticket, saying she believed Flake would lose because Trump supporters would not back Flake.

McDaniel said the RNC usually stayed out of primaries but under the party's bylaws could intervene if a number of RNC committee members agreed it was necessary.

"They need to have another candidate that they supported and the three RNC members that have to agree on that other candidate for rule 11 to apply, but it is in their bylaws," McDaniel said. "It's just interesting from a party standpoint, we do have governance. We have 168 members that they make those decisions. Sometimes you get in the nitty gritty, but I will say if you look at 2016, the senators that did not support the President, and let's look at Joe Heck and Kelly Ayotte, they fell short in those Senate races, so there is a cautionary tale there because voters want you to support the President in his agenda."

Read More