There’s a full-blown recall push brewing in Arizona ... with the local sheriff leading the search for Nancy Guthrie getting dragged over what critics are calling his "embarrassing" efforts ... and he isn't dodging the backlash.

The push to boot him is being led by Republican congressional candidate Daniel Butierez, who says the handling of the case by Pima County Sheriff Chris Nanos has been "embarrassing" across the board -- he's also throwing in claims the sheriff fudged parts of his employment history.

Sheriff Nanos admitted a recall is the public's right, saying ... "We’ll always honor the will of the people, and that’s what makes democracy." He's got some time to react, as Butierez mounts his organizational efforts ...

Butierez officially kicked things off last Thursday, giving himself 120 days to gather enough signatures to force Nanos out ... all while county officials are set to review questions about the sheriff’s employment history later this month.

Meanwhile, all this political chaos is unfolding against the backdrop of a much bigger issue -- the ongoing search for Savannah Guthrie’s mom, Nancy, who was abducted from her Tucson home in the middle of the night back on February 1.